(Bayesian Vector Autoregressive Models)=

Bayesian Vector Autoregressive Models

:::{post} November, 2022 :tags: time series, vector autoregressive model, hierarchical model :category: intermediate :author: Nathaniel Forde :::

import os

import arviz as az
import matplotlib.pyplot as plt
import numpy as np
import pandas as pd
import pymc as pm
import statsmodels.api as sm

from pymc.sampling_jax import sample_blackjax_nuts

/Users/nathanielforde/mambaforge/envs/myjlabenv/lib/python3.11/site-packages/pymc/sampling/jax.py:39: UserWarning: This module is experimental.
  warnings.warn("This module is experimental.")

RANDOM_SEED = 8927
rng = np.random.default_rng(RANDOM_SEED)
az.style.use("arviz-darkgrid")
%config InlineBackend.figure_format = 'retina'

V(ector)A(uto)R(egression) Models

In this notebook we will outline an application of the Bayesian Vector Autoregressive Modelling. We will draw on the work in the PYMC Labs blogpost (see {cite:t}vieira2022BVAR). This will be a three part series. In the first we want to show how to fit Bayesian VAR models in PYMC. In the second we will show how to extract extra insight from the fitted model with Impulse Response analysis and make forecasts from the fitted VAR model. In the third and final post we will show in some more detail the benefits of using hierarchical priors with Bayesian VAR models. Specifically, we'll outline how and why there are actually a range of carefully formulated industry standard priors which work with Bayesian VAR modelling.

In this post we will (i) demonstrate the basic pattern on a simple VAR model on fake data and show how the model recovers the true data generating parameters and (ii) we will show an example applied to macro-economic data and compare the results to those achieved on the same data with statsmodels MLE fits and (iii) show an example of estimating a hierarchical bayesian VAR model over a number of countries.

Autoregressive Models in General

The idea of a simple autoregressive model is to capture the manner in which past observations of the timeseries are predictive of the current observation. So in traditional fashion, if we model this as a linear phenomena we get simple autoregressive models where the current value is predicted by a weighted linear combination of the past values and an error term.

$$ y_t = \alpha + \beta_{y0} \cdot y_{t-1} + \beta_{y1} \cdot y_{t-2} ... + \epsilon $$

for however many lags are deemed appropriate to the predict the current observation.

A VAR model is kind of generalisation of this framework in that it retains the linear combination approach but allows us to model multiple timeseries at once. So concretely this mean that $\mathbf{y}_{t}$ as a vector where:

$$ \mathbf{y}_{T} = \nu + A_{1}\mathbf{y}_{T-1} + A_{2}\mathbf{y}_{T-2} ... A_{p}\mathbf{y}_{T-p} + \mathbf{e}_{t} $$

where the As are coefficient matrices to be combined with the past values of each individual timeseries. For example consider an economic example where we aim to model the relationship and mutual influence of each variable on themselves and one another.

$$ \begin{bmatrix} gdp \\ inv \\ con \end{bmatrix}_{T} = \nu + A_{1}\begin{bmatrix} gdp \\ inv \\ con \end{bmatrix}_{T-1} + A_{2}\begin{bmatrix} gdp \\ inv \\ con \end{bmatrix}_{T-2} ... A_{p}\begin{bmatrix} gdp \\ inv \\ con \end{bmatrix}_{T-p} + \mathbf{e}_{t} $$

This structure is compact representation using matrix notation. The thing we are trying to estimate when we fit a VAR model is the A matrices that determine the nature of the linear combination that best fits our timeseries data. Such timeseries models can have an auto-regressive or a moving average representation, and the details matter for some of the implication of a VAR model fit.

We'll see in the next notebook of the series how the moving-average representation of a VAR lends itself to the interpretation of the covariance structure in our model as representing a kind of impulse-response relationship between the component timeseries.

A Concrete Specification with Two lagged Terms

The matrix notation is convenient to suggest the broad patterns of the model, but it is useful to see the algebra is a simple case. Consider the case of Ireland's GDP and consumption described as:

$$ gdp_{t} = \beta_{gdp1} \cdot gdp_{t-1} + \beta_{gdp2} \cdot gdp_{t-2} + \beta_{cons1} \cdot cons_{t-1} + \beta_{cons2} \cdot cons_{t-2} + \epsilon_{gdp}$$$$ cons_{t} = \beta_{cons1} \cdot cons_{t-1} + \beta_{cons2} \cdot cons_{t-2} + \beta_{gdp1} \cdot gdp_{t-1} + \beta_{gdp2} \cdot gdp_{t-2} + \epsilon_{cons}$$

In this way we can see that if we can estimate the $\beta$ terms we have an estimate for the bi-directional effects of each variable on the other. This is a useful feature of the modelling. In what follows i should stress that i'm not an economist and I'm aiming to show only the functionality of these models not give you a decisive opinion about the economic relationships determining Irish GDP figures.

Creating some Fake Data

def simulate_var(
    intercepts, coefs_yy, coefs_xy, coefs_xx, coefs_yx, noises=(1, 1), *, warmup=100, steps=200
):
    draws_y = np.zeros(warmup + steps)
    draws_x = np.zeros(warmup + steps)
    draws_y[:2] = intercepts[0]
    draws_x[:2] = intercepts[1]
    for step in range(2, warmup + steps):
        draws_y[step] = (
            intercepts[0]
            + coefs_yy[0] * draws_y[step - 1]
            + coefs_yy[1] * draws_y[step - 2]
            + coefs_xy[0] * draws_x[step - 1]
            + coefs_xy[1] * draws_x[step - 2]
            + rng.normal(0, noises[0])
        )
        draws_x[step] = (
            intercepts[1]
            + coefs_xx[0] * draws_x[step - 1]
            + coefs_xx[1] * draws_x[step - 2]
            + coefs_yx[0] * draws_y[step - 1]
            + coefs_yx[1] * draws_y[step - 2]
            + rng.normal(0, noises[1])
        )
    return draws_y[warmup:], draws_x[warmup:]

First we generate some fake data with known parameters.

var_y, var_x = simulate_var(
    intercepts=(18, 8),
    coefs_yy=(-0.8, 0),
    coefs_xy=(0.9, 0),
    coefs_xx=(1.3, -0.7),
    coefs_yx=(-0.1, 0.3),
)

df = pd.DataFrame({"x": var_x, "y": var_y})
df.head()

	x	y
0	34.606613	30.117581
1	34.773803	23.996700
2	35.455237	29.738941
3	33.886706	27.193417
4	31.837465	26.704728

fig, axs = plt.subplots(2, 1, figsize=(10, 3))
axs[0].plot(df["x"], label="x")
axs[0].set_title("Series X")
axs[1].plot(df["y"], label="y")
axs[1].set_title("Series Y");

Handling Multiple Lags and Different Dimensions

When Modelling multiple timeseries and accounting for potentially any number lags to incorporate in our model we need to abstract some of the model definition to helper functions. An example will make this a bit clearer.

### Define a helper function that will construct our autoregressive step for the marginal contribution of each lagged
### term in each of the respective time series equations
def calc_ar_step(lag_coefs, n_eqs, n_lags, df):
    ars = []
    for j in range(n_eqs):
        ar = pm.math.sum(
            [
                pm.math.sum(lag_coefs[j, i] * df.values[n_lags - (i + 1) : -(i + 1)], axis=-1)
                for i in range(n_lags)
            ],
            axis=0,
        )
        ars.append(ar)
    beta = pm.math.stack(ars, axis=-1)

    return beta


### Make the model in such a way that it can handle different specifications of the likelihood term
### and can be run for simple prior predictive checks. This latter functionality is important for debugging of
### shape handling issues. Building a VAR model involves quite a few moving parts and it is handy to
### inspect the shape implied in the prior predictive checks.
def make_model(n_lags, n_eqs, df, priors, mv_norm=True, prior_checks=True):
    coords = {
        "lags": np.arange(n_lags) + 1,
        "equations": df.columns.tolist(),
        "cross_vars": df.columns.tolist(),
        "time": [x for x in df.index[n_lags:]],
    }

    with pm.Model(coords=coords) as model:
        lag_coefs = pm.Normal(
            "lag_coefs",
            mu=priors["lag_coefs"]["mu"],
            sigma=priors["lag_coefs"]["sigma"],
            dims=["equations", "lags", "cross_vars"],
        )
        alpha = pm.Normal(
            "alpha", mu=priors["alpha"]["mu"], sigma=priors["alpha"]["sigma"], dims=("equations",)
        )
        data_obs = pm.Data("data_obs", df.values[n_lags:], dims=["time", "equations"], mutable=True)

        betaX = calc_ar_step(lag_coefs, n_eqs, n_lags, df)
        betaX = pm.Deterministic(
            "betaX",
            betaX,
            dims=[
                "time",
            ],
        )
        mean = alpha + betaX

        if mv_norm:
            n = df.shape[1]
            ## Under the hood the LKJ prior will retain the correlation matrix too.
            noise_chol, _, _ = pm.LKJCholeskyCov(
                "noise_chol",
                eta=priors["noise_chol"]["eta"],
                n=n,
                sd_dist=pm.HalfNormal.dist(sigma=priors["noise_chol"]["sigma"]),
            )
            obs = pm.MvNormal(
                "obs", mu=mean, chol=noise_chol, observed=data_obs, dims=["time", "equations"]
            )
        else:
            ## This is an alternative likelihood that can recover sensible estimates of the coefficients
            ## But lacks the multivariate correlation between the timeseries.
            sigma = pm.HalfNormal("noise", sigma=priors["noise"]["sigma"], dims=["equations"])
            obs = pm.Normal(
                "obs", mu=mean, sigma=sigma, observed=data_obs, dims=["time", "equations"]
            )

        if prior_checks:
            idata = pm.sample_prior_predictive()
            return model, idata
        else:
            idata = pm.sample_prior_predictive()
            idata.extend(pm.sample(draws=2000, random_seed=130))
            pm.sample_posterior_predictive(idata, extend_inferencedata=True, random_seed=rng)
    return model, idata

The model has a deterministic component in the auto-regressive calculation which is required at each timestep, but the key point here is that we model the likelihood of the VAR as a multivariate normal distribution with a particular covariance relationship. The estimation of these covariance relationship gives the main insight in the manner in which our component timeseries relate to one another.

We will inspect the structure of a VAR with 2 lags and 2 equations

n_lags = 2
n_eqs = 2
priors = {
    "lag_coefs": {"mu": 0.3, "sigma": 1},
    "alpha": {"mu": 15, "sigma": 5},
    "noise_chol": {"eta": 1, "sigma": 1},
    "noise": {"sigma": 1},
}

model, idata = make_model(n_lags, n_eqs, df, priors)
pm.model_to_graphviz(model)

Sampling: [alpha, lag_coefs, noise_chol, obs]

Another VAR with 3 lags and 2 equations.

n_lags = 3
n_eqs = 2
model, idata = make_model(n_lags, n_eqs, df, priors)
for rv, shape in model.eval_rv_shapes().items():
    print(f"{rv:>11}: shape={shape}")
pm.model_to_graphviz(model)

Sampling: [alpha, lag_coefs, noise_chol, obs]

  lag_coefs: shape=(2, 3, 2)
      alpha: shape=(2,)
noise_chol_cholesky-cov-packed__: shape=(3,)
 noise_chol: shape=(3,)

We can inspect the correlation matrix between our timeseries which is implied by the prior specification, to see that we have allowed a flat uniform prior over their correlation.

ax = az.plot_posterior(
    idata,
    var_names="noise_chol_corr",
    hdi_prob="hide",
    group="prior",
    point_estimate="mean",
    grid=(2, 2),
    kind="hist",
    ec="black",
    figsize=(10, 4),
)

Now we will fit the VAR with 2 lags and 2 equations

n_lags = 2
n_eqs = 2
model, idata_fake_data = make_model(n_lags, n_eqs, df, priors, prior_checks=False)

Sampling: [alpha, lag_coefs, noise_chol, obs]
Auto-assigning NUTS sampler...
Initializing NUTS using jitter+adapt_diag...
Multiprocess sampling (4 chains in 4 jobs)
NUTS: [lag_coefs, alpha, noise_chol]

100.00% [12000/12000 05:59<00:00 Sampling 4 chains, 0 divergences]

Sampling 4 chains for 1_000 tune and 2_000 draw iterations (4_000 + 8_000 draws total) took 360 seconds.
Sampling: [obs]

100.00% [8000/8000 02:11<00:00]

We'll now plot some of the results to see that the parameters are being broadly recovered. The alpha parameters match well, but the individual lag coefficients show differences.

az.summary(idata_fake_data, var_names=["alpha", "lag_coefs", "noise_chol_corr"])

/Users/nathanielforde/mambaforge/envs/myjlabenv/lib/python3.11/site-packages/arviz/stats/diagnostics.py:584: RuntimeWarning: invalid value encountered in scalar divide
  (between_chain_variance / within_chain_variance + num_samples - 1) / (num_samples)

	mean	sd	hdi_3%	hdi_97%	mcse_mean	mcse_sd	ess_bulk	ess_tail	r_hat
alpha[x]	8.607	1.765	5.380	12.076	0.029	0.020	3823.0	4602.0	1.0
alpha[y]	17.094	1.778	13.750	20.431	0.027	0.019	4188.0	5182.0	1.0
lag_coefs[x, 1, x]	1.333	0.062	1.218	1.450	0.001	0.001	5564.0	4850.0	1.0
lag_coefs[x, 1, y]	-0.120	0.069	-0.247	0.011	0.001	0.001	3739.0	4503.0	1.0
lag_coefs[x, 2, x]	-0.711	0.097	-0.890	-0.527	0.002	0.001	3629.0	4312.0	1.0
lag_coefs[x, 2, y]	0.267	0.073	0.126	0.403	0.001	0.001	3408.0	4318.0	1.0
lag_coefs[y, 1, x]	0.838	0.061	0.718	0.948	0.001	0.001	5203.0	5345.0	1.0
lag_coefs[y, 1, y]	-0.800	0.069	-0.932	-0.673	0.001	0.001	3749.0	5131.0	1.0
lag_coefs[y, 2, x]	0.094	0.097	-0.087	0.277	0.002	0.001	3573.0	4564.0	1.0
lag_coefs[y, 2, y]	-0.004	0.074	-0.145	0.133	0.001	0.001	3448.0	4484.0	1.0
noise_chol_corr[0, 0]	1.000	0.000	1.000	1.000	0.000	0.000	8000.0	8000.0	NaN
noise_chol_corr[0, 1]	0.021	0.072	-0.118	0.152	0.001	0.001	6826.0	5061.0	1.0
noise_chol_corr[1, 0]	0.021	0.072	-0.118	0.152	0.001	0.001	6826.0	5061.0	1.0
noise_chol_corr[1, 1]	1.000	0.000	1.000	1.000	0.000	0.000	7813.0	7824.0	1.0

az.plot_posterior(idata_fake_data, var_names=["alpha"], ref_val=[8, 18]);

Next we'll plot the posterior predictive distribution to check that the fitted model can capture the patterns in the observed data. This is the primary test of goodness of fit.

def shade_background(ppc, ax, idx, palette="cividis"):
    palette = palette
    cmap = plt.get_cmap(palette)
    percs = np.linspace(51, 99, 100)
    colors = (percs - np.min(percs)) / (np.max(percs) - np.min(percs))
    for i, p in enumerate(percs[::-1]):
        upper = np.percentile(
            ppc[:, idx, :],
            p,
            axis=1,
        )
        lower = np.percentile(
            ppc[:, idx, :],
            100 - p,
            axis=1,
        )
        color_val = colors[i]
        ax[idx].fill_between(
            x=np.arange(ppc.shape[0]),
            y1=upper.flatten(),
            y2=lower.flatten(),
            color=cmap(color_val),
            alpha=0.1,
        )


def plot_ppc(idata, df, group="posterior_predictive"):
    fig, axs = plt.subplots(2, 1, figsize=(25, 15))
    df = pd.DataFrame(idata_fake_data["observed_data"]["obs"].data, columns=["x", "y"])
    axs = axs.flatten()
    ppc = az.extract(idata, group=group, num_samples=100)["obs"]
    # Minus the lagged terms and the constant
    shade_background(ppc, axs, 0, "inferno")
    axs[0].plot(np.arange(ppc.shape[0]), ppc[:, 0, :].mean(axis=1), color="cyan", label="Mean")
    axs[0].plot(df["x"], "o", mfc="black", mec="white", mew=1, markersize=7, label="Observed")
    axs[0].set_title("VAR Series 1")
    axs[0].legend()
    shade_background(ppc, axs, 1, "inferno")
    axs[1].plot(df["y"], "o", mfc="black", mec="white", mew=1, markersize=7, label="Observed")
    axs[1].plot(np.arange(ppc.shape[0]), ppc[:, 1, :].mean(axis=1), color="cyan", label="Mean")
    axs[1].set_title("VAR Series 2")
    axs[1].legend()


plot_ppc(idata_fake_data, df)

Again we can check the learned posterior distribution for the correlation parameter.

ax = az.plot_posterior(
    idata_fake_data,
    var_names="noise_chol_corr",
    hdi_prob="hide",
    point_estimate="mean",
    grid=(2, 2),
    kind="hist",
    ec="black",
    figsize=(10, 6),
)

Applying the Theory: Macro Economic Timeseries

The data is from the World Bank’s World Development Indicators. In particular, we're pulling annual values of GDP, consumption, and gross fixed capital formation (investment) for all countries from 1970. Timeseries models in general work best when we have a stable mean throughout the series, so for the estimation procedure we have taken the first difference and the natural log of each of these series.

try:
    gdp_hierarchical = pd.read_csv(
        os.path.join("..", "data", "gdp_data_hierarchical_clean.csv"), index_col=0
    )
except FileNotFoundError:
    gdp_hierarchical = pd.read_csv(pm.get_data("gdp_data_hierarchical_clean.csv"), ...)

gdp_hierarchical

	country	iso2c	iso3c	year	GDP	CONS	GFCF	dl_gdp	dl_cons	dl_gfcf	more_than_10	time
1	Australia	AU	AUS	1971	4.647670e+11	3.113170e+11	7.985100e+10	0.039217	0.040606	0.031705	True	1
2	Australia	AU	AUS	1972	4.829350e+11	3.229650e+11	8.209200e+10	0.038346	0.036732	0.027678	True	2
3	Australia	AU	AUS	1973	4.955840e+11	3.371070e+11	8.460300e+10	0.025855	0.042856	0.030129	True	3
4	Australia	AU	AUS	1974	5.159300e+11	3.556010e+11	8.821400e+10	0.040234	0.053409	0.041796	True	4
5	Australia	AU	AUS	1975	5.228210e+11	3.759000e+11	8.255900e+10	0.013268	0.055514	-0.066252	True	5
...	...	...	...	...	...	...	...	...	...	...	...	...
366	United States	US	USA	2016	1.850960e+13	1.522497e+13	3.802207e+12	0.016537	0.023425	0.021058	True	44
367	United States	US	USA	2017	1.892712e+13	1.553075e+13	3.947418e+12	0.022306	0.019885	0.037480	True	45
368	United States	US	USA	2018	1.947957e+13	1.593427e+13	4.119951e+12	0.028771	0.025650	0.042780	True	46
369	United States	US	USA	2019	1.992544e+13	1.627888e+13	4.248643e+12	0.022631	0.021396	0.030758	True	47
370	United States	US	USA	2020	1.924706e+13	1.582501e+13	4.182801e+12	-0.034639	-0.028277	-0.015619	True	48

370 rows × 12 columns

fig, axs = plt.subplots(3, 1, figsize=(20, 10))
for country in gdp_hierarchical["country"].unique():
    temp = gdp_hierarchical[gdp_hierarchical["country"] == country].reset_index()
    axs[0].plot(temp["dl_gdp"], label=f"{country}")
    axs[1].plot(temp["dl_cons"], label=f"{country}")
    axs[2].plot(temp["dl_gfcf"], label=f"{country}")
axs[0].set_title("Differenced and Logged GDP")
axs[1].set_title("Differenced and Logged Consumption")
axs[2].set_title("Differenced and Logged Investment")
axs[0].legend()
axs[1].legend()
axs[2].legend()
plt.suptitle("Macroeconomic Timeseries");

Ireland's Economic Situation

Ireland is somewhat infamous for its GDP numbers that are largely the product of foreign direct investment and inflated beyond expectation in recent years by the investment and taxation deals offered to large multi-nationals. We'll look here at just the relationship between GDP and consumption. We just want to show the mechanics of the VAR estimation, you shouldn't read too much into the subsequent analysis.

ireland_df = gdp_hierarchical[gdp_hierarchical["country"] == "Ireland"]
ireland_df.reset_index(inplace=True, drop=True)
ireland_df.head()

	country	iso2c	iso3c	year	GDP	CONS	GFCF	dl_gdp	dl_cons	dl_gfcf	more_than_10	time
0	Ireland	IE	IRL	1971	3.314234e+10	2.897699e+10	8.317518e+09	0.034110	0.043898	0.085452	True	1
1	Ireland	IE	IRL	1972	3.529322e+10	3.063538e+10	8.967782e+09	0.062879	0.055654	0.075274	True	2
2	Ireland	IE	IRL	1973	3.695956e+10	3.280221e+10	1.041728e+10	0.046134	0.068340	0.149828	True	3
3	Ireland	IE	IRL	1974	3.853412e+10	3.381524e+10	9.207243e+09	0.041720	0.030416	-0.123476	True	4
4	Ireland	IE	IRL	1975	4.071386e+10	3.477232e+10	8.874887e+09	0.055024	0.027910	-0.036765	True	5

n_lags = 2
n_eqs = 2
priors = {
    ## Set prior for expected positive relationship between the variables.
    "lag_coefs": {"mu": 0.3, "sigma": 1},
    "alpha": {"mu": 0, "sigma": 0.1},
    "noise_chol": {"eta": 1, "sigma": 1},
    "noise": {"sigma": 1},
}
model, idata_ireland = make_model(
    n_lags, n_eqs, ireland_df[["dl_gdp", "dl_cons"]], priors, prior_checks=False
)
idata_ireland

Sampling: [alpha, lag_coefs, noise_chol, obs]
Auto-assigning NUTS sampler...
Initializing NUTS using jitter+adapt_diag...
Multiprocess sampling (4 chains in 4 jobs)
NUTS: [lag_coefs, alpha, noise_chol]

100.00% [12000/12000 00:35<00:00 Sampling 4 chains, 0 divergences]

Sampling 4 chains for 1_000 tune and 2_000 draw iterations (4_000 + 8_000 draws total) took 36 seconds.
Sampling: [obs]

100.00% [8000/8000 00:33<00:00]

arviz.InferenceData

• posterior

  <xarray.Dataset>
  Dimensions:                (chain: 4, draw: 2000, equations: 2, lags: 2,
                              cross_vars: 2, noise_chol_dim_0: 3, time: 49,
                              betaX_dim_1: 2, noise_chol_corr_dim_0: 2,
                              noise_chol_corr_dim_1: 2, noise_chol_stds_dim_0: 2)
  Coordinates:
    * chain                  (chain) int64 0 1 2 3
    * draw                   (draw) int64 0 1 2 3 4 5 ... 1995 1996 1997 1998 1999
    * equations              (equations) <U7 'dl_gdp' 'dl_cons'
    * lags                   (lags) int64 1 2
    * cross_vars             (cross_vars) <U7 'dl_gdp' 'dl_cons'
    * noise_chol_dim_0       (noise_chol_dim_0) int64 0 1 2
    * time                   (time) int64 2 3 4 5 6 7 8 9 ... 44 45 46 47 48 49 50
    * betaX_dim_1            (betaX_dim_1) int64 0 1
    * noise_chol_corr_dim_0  (noise_chol_corr_dim_0) int64 0 1
    * noise_chol_corr_dim_1  (noise_chol_corr_dim_1) int64 0 1
    * noise_chol_stds_dim_0  (noise_chol_stds_dim_0) int64 0 1
  Data variables:
      lag_coefs              (chain, draw, equations, lags, cross_vars) float64 ...
      alpha                  (chain, draw, equations) float64 0.01472 ... 0.01042
      noise_chol             (chain, draw, noise_chol_dim_0) float64 0.04206 .....
      betaX                  (chain, draw, time, betaX_dim_1) float64 0.03846 ....
      noise_chol_corr        (chain, draw, noise_chol_corr_dim_0, noise_chol_corr_dim_1) float64 ...
      noise_chol_stds        (chain, draw, noise_chol_stds_dim_0) float64 0.042...
  Attributes:
      created_at:                 2023-02-21T19:21:22.942792
      arviz_version:              0.14.0
      inference_library:          pymc
      inference_library_version:  5.0.1
      sampling_time:              36.195340156555176
      tuning_steps:               1000

  xarray.Dataset

  • Dimensions:
    • chain: 4
    • draw: 2000
    • equations: 2
    • lags: 2
    • cross_vars: 2
    • noise_chol_dim_0: 3
    • time: 49
    • betaX_dim_1: 2
    • noise_chol_corr_dim_0: 2
    • noise_chol_corr_dim_1: 2
    • noise_chol_stds_dim_0: 2
  • Coordinates: (11)
    • chain
      (chain)
      int64
      0 1 2 3

      array([0, 1, 2, 3])

    • draw
      (draw)
      int64
      0 1 2 3 4 ... 1996 1997 1998 1999

      array([   0,    1,    2, ..., 1997, 1998, 1999])

    • equations
      (equations)
      <U7
      'dl_gdp' 'dl_cons'

      array(['dl_gdp', 'dl_cons'], dtype='<U7')

    • lags
      (lags)
      int64
      1 2

      array([1, 2])

    • cross_vars
      (cross_vars)
      <U7
      'dl_gdp' 'dl_cons'

      array(['dl_gdp', 'dl_cons'], dtype='<U7')

    • noise_chol_dim_0
      (noise_chol_dim_0)
      int64
      0 1 2

      array([0, 1, 2])

    • time
      (time)
      int64
      2 3 4 5 6 7 8 ... 45 46 47 48 49 50

      array([ 2,  3,  4,  5,  6,  7,  8,  9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19,
             20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37,
             38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50])

    • betaX_dim_1
      (betaX_dim_1)
      int64
      0 1

      array([0, 1])

    • noise_chol_corr_dim_0
      (noise_chol_corr_dim_0)
      int64
      0 1

      array([0, 1])

    • noise_chol_corr_dim_1
      (noise_chol_corr_dim_1)
      int64
      0 1

      array([0, 1])

    • noise_chol_stds_dim_0
      (noise_chol_stds_dim_0)
      int64
      0 1

      array([0, 1])

  • Data variables: (6)
    • lag_coefs
      (chain, draw, equations, lags, cross_vars)
      float64
      0.5197 0.07935 ... -0.2045 0.235

      array([[[[[ 5.19656576e-01,  7.93542008e-02],
                [ 2.61607049e-01, -1.72153516e-01]],
      
               [[ 3.58280690e-01,  4.69430533e-01],
                [-1.41598877e-02,  7.07116179e-02]]],
      
      
              [[[-4.16577591e-02,  4.06592634e-01],
                [ 3.42706574e-01, -5.74590855e-01]],
      
               [[ 3.79750238e-01,  3.33743286e-01],
                [-1.00207466e-01,  1.43191909e-01]]],
      
      
              [[[ 5.15113761e-01,  5.43954306e-02],
                [ 2.24354001e-01, -1.25071225e-01]],
      
               [[ 3.35089469e-01,  3.15187746e-01],
                [ 8.77271295e-05,  1.81655203e-01]]],
      
      ...
      
              [[[ 2.78892253e-01,  2.13837349e-01],
                [ 2.60725950e-01, -1.27187687e-01]],
      
               [[ 3.84079652e-01,  9.48802792e-02],
                [-2.23869617e-02,  2.29483840e-01]]],
      
      
              [[[ 6.31173009e-01, -5.28215508e-01],
                [-1.55673631e-01,  3.61610751e-02]],
      
               [[ 3.27117933e-01,  4.42098735e-01],
                [-1.36438735e-01, -5.36320280e-03]]],
      
      
              [[[ 4.27130277e-01, -2.91019063e-01],
                [ 2.63469903e-02,  2.47138008e-01]],
      
               [[ 4.50003809e-01,  7.52912358e-02],
                [-2.04480247e-01,  2.35021007e-01]]]]])

    • alpha
      (chain, draw, equations)
      float64
      0.01472 -0.001526 ... 0.01042

      array([[[ 0.01471676, -0.00152568],
              [ 0.0441433 ,  0.00203566],
              [ 0.01079889, -0.00421006],
              ...,
              [ 0.01721974,  0.00564757],
              [ 0.04886959,  0.00799192],
              [ 0.01667415,  0.00371018]],
      
             [[ 0.04548506,  0.01127504],
              [ 0.04432491, -0.00028508],
              [ 0.03517707,  0.01830341],
              ...,
              [ 0.01805819, -0.00392762],
              [ 0.05267103,  0.02336937],
              [ 0.04478405,  0.01691428]],
      
             [[ 0.03111884,  0.00949071],
              [ 0.04501899,  0.00520666],
              [ 0.03759947,  0.00563301],
              ...,
              [ 0.02761799,  0.00727374],
              [ 0.04597957,  0.01626677],
              [ 0.05225605,  0.01325381]],
      
             [[ 0.0365445 ,  0.00588842],
              [ 0.05292467,  0.01589702],
              [ 0.05850131,  0.00710232],
              ...,
              [ 0.03053105,  0.00836573],
              [ 0.02544402,  0.00399799],
              [ 0.03312685,  0.01041744]]])

    • noise_chol
      (chain, draw, noise_chol_dim_0)
      float64
      0.04206 0.01468 ... 0.01262 0.02424

      array([[[0.04205913, 0.01467698, 0.02638489],
              [0.03959323, 0.00462671, 0.02231385],
              [0.03619061, 0.0115924 , 0.02253414],
              ...,
              [0.04634195, 0.01092772, 0.02286984],
              [0.04250194, 0.01037661, 0.02405165],
              [0.04079687, 0.00585382, 0.02524456]],
      
             [[0.04310706, 0.00775202, 0.02517299],
              [0.04330754, 0.01079034, 0.02413016],
              [0.03938486, 0.01259796, 0.02279358],
              ...,
              [0.04874519, 0.01286422, 0.02864554],
              [0.04704716, 0.01101798, 0.02170003],
              [0.04075767, 0.001405  , 0.02298114]],
      
             [[0.04082337, 0.00868785, 0.0205891 ],
              [0.04190526, 0.0087839 , 0.02398674],
              [0.0479445 , 0.01780939, 0.0228716 ],
              ...,
              [0.04367215, 0.00381667, 0.02414608],
              [0.04618374, 0.00985851, 0.0241093 ],
              [0.04771735, 0.01976765, 0.02301084]],
      
             [[0.03937039, 0.01452327, 0.02261826],
              [0.04017701, 0.00773141, 0.01975944],
              [0.04501176, 0.00872818, 0.01975194],
              ...,
              [0.04350486, 0.00854354, 0.02546362],
              [0.04543641, 0.01214901, 0.023637  ],
              [0.04664034, 0.01261794, 0.02423548]]])

    • betaX
      (chain, draw, time, betaX_dim_1)
      float64
      0.03846 0.05127 ... 0.05137 0.02155

      array([[[[ 0.03845828,  0.05127494],
               [ 0.03626535,  0.0516547 ],
               [ 0.02439747,  0.03340475],
               ...,
               [ 0.06606994,  0.05073041],
               [ 0.04383074,  0.03827857],
               [ 0.03082664, -0.00237368]],
      
              [[ 0.0064756 ,  0.04532004],
               [ 0.01543582,  0.04199548],
               [-0.0128284 ,  0.03115703],
               ...,
               [ 0.027321  ,  0.04158131],
               [ 0.02104586,  0.02920793],
               [-0.03139562,  0.00495901]],
      
              [[ 0.03757968,  0.04658869],
               [ 0.03462795,  0.04711412],
               [ 0.0249478 ,  0.03598497],
               ...,
      ...
               ...,
               [ 0.05183073,  0.04113899],
               [ 0.03959469,  0.02977498],
               [ 0.01174284,  0.02525658]],
      
              [[ 0.00656781,  0.04028385],
               [-0.01475617,  0.03642657],
               [ 0.00555572,  0.0204332 ],
               ...,
               [ 0.02066245,  0.03446825],
               [-0.00354691,  0.02198112],
               [ 0.05819251, -0.01170932]],
      
              [[ 0.02240881,  0.03582803],
               [ 0.01522756,  0.02612792],
               [ 0.0270731 ,  0.02769207],
               ...,
               [ 0.03377353,  0.03059268],
               [ 0.0208055 ,  0.01661153],
               [ 0.05137065,  0.02154906]]]])

    • noise_chol_corr
      (chain, draw, noise_chol_corr_dim_0, noise_chol_corr_dim_1)
      float64
      1.0 0.4861 0.4861 ... 0.4618 1.0

      array([[[[1.        , 0.48611626],
               [0.48611626, 1.        ]],
      
              [[1.        , 0.20302855],
               [0.20302855, 1.        ]],
      
              [[1.        , 0.45745439],
               [0.45745439, 1.        ]],
      
              ...,
      
              [[1.        , 0.43113357],
               [0.43113357, 1.        ]],
      
              [[1.        , 0.39613595],
               [0.39613595, 1.        ]],
      
              [[1.        , 0.22589091],
               [0.22589091, 1.        ]]],
      
      ...
      
             [[[1.        , 0.54030892],
               [0.54030892, 1.        ]],
      
              [[1.        , 0.36437699],
               [0.36437699, 1.        ]],
      
              [[1.        , 0.40418614],
               [0.40418614, 1.        ]],
      
              ...,
      
              [[1.        , 0.31809258],
               [0.31809258, 1.        ]],
      
              [[1.        , 0.45713496],
               [0.45713496, 1.        ]],
      
              [[1.        , 0.46179879],
               [0.46179879, 1.        ]]]])

    • noise_chol_stds
      (chain, draw, noise_chol_stds_dim_0)
      float64
      0.04206 0.03019 ... 0.04664 0.02732

      array([[[0.04205913, 0.03019232],
              [0.03959323, 0.02278847],
              [0.03619061, 0.0253411 ],
              ...,
              [0.04634195, 0.02534649],
              [0.04250194, 0.02619458],
              [0.04079687, 0.02591438]],
      
             [[0.04310706, 0.02633958],
              [0.04330754, 0.02643286],
              [0.03938486, 0.02604334],
              ...,
              [0.04874519, 0.03140152],
              [0.04704716, 0.02433695],
              [0.04075767, 0.02302405]],
      
             [[0.04082337, 0.02234703],
              [0.04190526, 0.02554449],
              [0.0479445 , 0.02898766],
              ...,
              [0.04367215, 0.02444586],
              [0.04618374, 0.02604704],
              [0.04771735, 0.03033577]],
      
             [[0.03937039, 0.02687956],
              [0.04017701, 0.02121816],
              [0.04501176, 0.02159444],
              ...,
              [0.04350486, 0.02685867],
              [0.04543641, 0.02657642],
              [0.04664034, 0.02732345]]])

  • Indexes: (11)
    • chain
      PandasIndex

      PandasIndex(Int64Index([0, 1, 2, 3], dtype='int64', name='chain'))

    • draw
      PandasIndex

      PandasIndex(Int64Index([   0,    1,    2,    3,    4,    5,    6,    7,    8,    9,
                  ...
                  1990, 1991, 1992, 1993, 1994, 1995, 1996, 1997, 1998, 1999],
                 dtype='int64', name='draw', length=2000))

    • equations
      PandasIndex

      PandasIndex(Index(['dl_gdp', 'dl_cons'], dtype='object', name='equations'))

    • lags
      PandasIndex

      PandasIndex(Int64Index([1, 2], dtype='int64', name='lags'))

    • cross_vars
      PandasIndex

      PandasIndex(Index(['dl_gdp', 'dl_cons'], dtype='object', name='cross_vars'))

    • noise_chol_dim_0
      PandasIndex

      PandasIndex(Int64Index([0, 1, 2], dtype='int64', name='noise_chol_dim_0'))

    • time
      PandasIndex

      PandasIndex(Int64Index([ 2,  3,  4,  5,  6,  7,  8,  9, 10, 11, 12, 13, 14, 15, 16, 17, 18,
                  19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35,
                  36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50],
                 dtype='int64', name='time'))

    • betaX_dim_1
      PandasIndex

      PandasIndex(Int64Index([0, 1], dtype='int64', name='betaX_dim_1'))

    • noise_chol_corr_dim_0
      PandasIndex

      PandasIndex(Int64Index([0, 1], dtype='int64', name='noise_chol_corr_dim_0'))

    • noise_chol_corr_dim_1
      PandasIndex

      PandasIndex(Int64Index([0, 1], dtype='int64', name='noise_chol_corr_dim_1'))

    • noise_chol_stds_dim_0
      PandasIndex

      PandasIndex(Int64Index([0, 1], dtype='int64', name='noise_chol_stds_dim_0'))

  • Attributes: (6)

    created_at :

    2023-02-21T19:21:22.942792

    arviz_version :

    0.14.0

    inference_library :

    pymc

    inference_library_version :

    5.0.1

    sampling_time :

    36.195340156555176

    tuning_steps :

    1000

  
  
• posterior_predictive

  <xarray.Dataset>
  Dimensions:    (chain: 4, draw: 2000, time: 49, equations: 2)
  Coordinates:
    * chain      (chain) int64 0 1 2 3
    * draw       (draw) int64 0 1 2 3 4 5 6 ... 1993 1994 1995 1996 1997 1998 1999
    * time       (time) int64 2 3 4 5 6 7 8 9 10 11 ... 42 43 44 45 46 47 48 49 50
    * equations  (equations) <U7 'dl_gdp' 'dl_cons'
  Data variables:
      obs        (chain, draw, time, equations) float64 0.07266 ... 0.05994
  Attributes:
      created_at:                 2023-02-21T19:21:57.788979
      arviz_version:              0.14.0
      inference_library:          pymc
      inference_library_version:  5.0.1

  xarray.Dataset

  • Dimensions:
    • chain: 4
    • draw: 2000
    • time: 49
    • equations: 2
  • Coordinates: (4)
    • chain
      (chain)
      int64
      0 1 2 3

      array([0, 1, 2, 3])

    • draw
      (draw)
      int64
      0 1 2 3 4 ... 1996 1997 1998 1999

      array([   0,    1,    2, ..., 1997, 1998, 1999])

    • time
      (time)
      int64
      2 3 4 5 6 7 8 ... 45 46 47 48 49 50

      array([ 2,  3,  4,  5,  6,  7,  8,  9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19,
             20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37,
             38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50])

    • equations
      (equations)
      <U7
      'dl_gdp' 'dl_cons'

      array(['dl_gdp', 'dl_cons'], dtype='<U7')

  • Data variables: (1)
    • obs
      (chain, draw, time, equations)
      float64
      0.07266 0.05554 ... 0.131 0.05994

      array([[[[ 0.07266384,  0.05554043],
               [-0.03723739, -0.01044936],
               [ 0.06613757,  0.01211585],
               ...,
               [ 0.13244691,  0.06005397],
               [-0.02656575,  0.02116827],
               [ 0.07340778,  0.01205019]],
      
              [[ 0.08268452,  0.01698459],
               [ 0.02978633,  0.01275627],
               [ 0.01878881,  0.04764196],
               ...,
               [ 0.12656091,  0.00217327],
               [ 0.04914098, -0.00649668],
               [ 0.03080986,  0.05185062]],
      
              [[ 0.02621489,  0.00719224],
               [ 0.01166067,  0.0217407 ],
               [ 0.06380577,  0.06132611],
               ...,
      ...
               ...,
               [ 0.13366362,  0.0631761 ],
               [ 0.08309923,  0.10108214],
               [ 0.02315299,  0.02944125]],
      
              [[ 0.10004432,  0.08094177],
               [ 0.02037102,  0.08725727],
               [ 0.00521511,  0.03733144],
               ...,
               [ 0.05345503,  0.08313247],
               [ 0.03175078,  0.01423723],
               [ 0.16007207, -0.04465602]],
      
              [[ 0.05437818,  0.0252325 ],
               [ 0.08520019,  0.04364142],
               [ 0.02855142,  0.03297121],
               ...,
               [ 0.15104638,  0.08219397],
               [ 0.1100447 ,  0.010313  ],
               [ 0.13102166,  0.05993663]]]])

  • Indexes: (4)
    • chain
      PandasIndex

      PandasIndex(Int64Index([0, 1, 2, 3], dtype='int64', name='chain'))

    • draw
      PandasIndex

      PandasIndex(Int64Index([   0,    1,    2,    3,    4,    5,    6,    7,    8,    9,
                  ...
                  1990, 1991, 1992, 1993, 1994, 1995, 1996, 1997, 1998, 1999],
                 dtype='int64', name='draw', length=2000))

    • time
      PandasIndex

      PandasIndex(Int64Index([ 2,  3,  4,  5,  6,  7,  8,  9, 10, 11, 12, 13, 14, 15, 16, 17, 18,
                  19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35,
                  36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50],
                 dtype='int64', name='time'))

    • equations
      PandasIndex

      PandasIndex(Index(['dl_gdp', 'dl_cons'], dtype='object', name='equations'))

  • Attributes: (4)

    created_at :

    2023-02-21T19:21:57.788979

    arviz_version :

    0.14.0

    inference_library :

    pymc

    inference_library_version :

    5.0.1

  
  
• sample_stats

  <xarray.Dataset>
  Dimensions:                (chain: 4, draw: 2000)
  Coordinates:
    * chain                  (chain) int64 0 1 2 3
    * draw                   (draw) int64 0 1 2 3 4 5 ... 1995 1996 1997 1998 1999
  Data variables: (12/17)
      step_size              (chain, draw) float64 0.2559 0.2559 ... 0.2865 0.2865
      perf_counter_start     (chain, draw) float64 1.626e+05 ... 1.626e+05
      acceptance_rate        (chain, draw) float64 0.452 0.882 ... 0.6842 0.6953
      largest_eigval         (chain, draw) float64 nan nan nan nan ... nan nan nan
      lp                     (chain, draw) float64 192.2 189.8 ... 185.6 191.9
      n_steps                (chain, draw) float64 15.0 15.0 15.0 ... 15.0 15.0
      ...                     ...
      energy_error           (chain, draw) float64 0.1063 -0.1922 ... -0.8926
      diverging              (chain, draw) bool False False False ... False False
      index_in_trajectory    (chain, draw) int64 8 -6 -6 -6 10 ... 10 10 -10 -6
      energy                 (chain, draw) float64 -186.7 -183.7 ... -182.6 -182.3
      process_time_diff      (chain, draw) float64 0.007787 0.01354 ... 0.01025
      reached_max_treedepth  (chain, draw) bool False False False ... False False
  Attributes:
      created_at:                 2023-02-21T19:21:22.951462
      arviz_version:              0.14.0
      inference_library:          pymc
      inference_library_version:  5.0.1
      sampling_time:              36.195340156555176
      tuning_steps:               1000

  xarray.Dataset

  • Dimensions:
    • chain: 4
    • draw: 2000
  • Coordinates: (2)
    • chain
      (chain)
      int64
      0 1 2 3

      array([0, 1, 2, 3])

    • draw
      (draw)
      int64
      0 1 2 3 4 ... 1996 1997 1998 1999

      array([   0,    1,    2, ..., 1997, 1998, 1999])

  • Data variables: (17)
    • step_size
      (chain, draw)
      float64
      0.2559 0.2559 ... 0.2865 0.2865

      array([[0.25588962, 0.25588962, 0.25588962, ..., 0.25588962, 0.25588962,
              0.25588962],
             [0.3697469 , 0.3697469 , 0.3697469 , ..., 0.3697469 , 0.3697469 ,
              0.3697469 ],
             [0.42101555, 0.42101555, 0.42101555, ..., 0.42101555, 0.42101555,
              0.42101555],
             [0.28653149, 0.28653149, 0.28653149, ..., 0.28653149, 0.28653149,
              0.28653149]])

    • perf_counter_start
      (chain, draw)
      float64
      1.626e+05 1.626e+05 ... 1.626e+05

      array([[162631.64961679, 162631.65651296, 162631.66551496, ...,
              162648.95160179, 162648.95829438, 162648.96578838],
             [162631.04184112, 162631.05123112, 162631.0605795 , ...,
              162648.36295925, 162648.37161829, 162648.37843467],
             [162632.29036962, 162632.30043392, 162632.30901504, ...,
              162649.81244104, 162649.81932071, 162649.8258015 ],
             [162631.24282437, 162631.25291775, 162631.26280779, ...,
              162648.34229779, 162648.35076021, 162648.35829229]])

    • acceptance_rate
      (chain, draw)
      float64
      0.452 0.882 ... 0.6842 0.6953

      array([[0.45200921, 0.88196032, 0.85477008, ..., 0.96927221, 0.84755787,
              0.72968371],
             [0.98771315, 0.8009883 , 0.80420022, ..., 0.86016188, 0.75991948,
              0.20906901],
             [0.99751756, 0.9866047 , 0.73547533, ..., 0.95386729, 0.73301308,
              0.6478722 ],
             [0.97393312, 0.4316111 , 0.35684925, ..., 0.95519091, 0.6841993 ,
              0.69534805]])

    • largest_eigval
      (chain, draw)
      float64
      nan nan nan nan ... nan nan nan nan

      array([[nan, nan, nan, ..., nan, nan, nan],
             [nan, nan, nan, ..., nan, nan, nan],
             [nan, nan, nan, ..., nan, nan, nan],
             [nan, nan, nan, ..., nan, nan, nan]])

    • lp
      (chain, draw)
      float64
      192.2 189.8 192.1 ... 185.6 191.9

      array([[192.18966643, 189.81728435, 192.14034097, ..., 192.06668954,
              193.42245096, 191.36656983],
             [190.79957544, 190.83997606, 187.12480105, ..., 185.29102408,
              187.45700699, 188.40205797],
             [192.65934246, 194.23007138, 192.32551615, ..., 192.41982885,
              189.68059219, 187.40005344],
             [193.08342569, 191.03132672, 188.24977915, ..., 191.53209216,
              185.60644058, 191.94696886]])

    • n_steps
      (chain, draw)
      float64
      15.0 15.0 15.0 ... 15.0 15.0 15.0

      array([[15., 15., 15., ..., 15., 15., 15.],
             [15., 15., 15., ..., 15., 15., 15.],
             [15., 15., 15., ..., 15., 15., 15.],
             [15., 15., 15., ..., 15., 15., 15.]])

    • perf_counter_diff
      (chain, draw)
      float64
      0.006816 0.00892 ... 0.009416

      array([[0.00681596, 0.00891987, 0.00853138, ..., 0.00662113, 0.00743258,
              0.00674708],
             [0.00924708, 0.00926471, 0.00896663, ..., 0.00856346, 0.00672742,
              0.00760842],
             [0.00998017, 0.0084875 , 0.00804771, ..., 0.00681546, 0.00641321,
              0.00689512],
             [0.01000392, 0.0098055 , 0.00847175, ..., 0.008375  , 0.00745308,
              0.00941558]])

    • max_energy_error
      (chain, draw)
      float64
      2.216 0.4151 0.2987 ... 1.156 1.252

      array([[ 2.21643644,  0.41508426,  0.29868443, ..., -0.09954207,
               0.39111492,  0.94939641],
             [-0.23714436,  0.34132827,  0.66750119, ...,  0.33884617,
               1.38906123,  4.3288482 ],
             [-0.13750741, -0.07262999,  0.49443942, ..., -0.80694987,
               0.63095501,  0.99504025],
             [-0.1666122 ,  2.17550408,  3.13785432, ..., -0.33376487,
               1.15567682,  1.25234077]])

    • tree_depth
      (chain, draw)
      int64
      4 4 4 4 4 4 4 4 ... 4 4 4 4 4 4 4 4

      array([[4, 4, 4, ..., 4, 4, 4],
             [4, 4, 4, ..., 4, 4, 4],
             [4, 4, 4, ..., 4, 4, 4],
             [4, 4, 4, ..., 4, 4, 4]])

    • step_size_bar
      (chain, draw)
      float64
      0.2629 0.2629 ... 0.2741 0.2741

      array([[0.26288954, 0.26288954, 0.26288954, ..., 0.26288954, 0.26288954,
              0.26288954],
             [0.28887259, 0.28887259, 0.28887259, ..., 0.28887259, 0.28887259,
              0.28887259],
             [0.26055628, 0.26055628, 0.26055628, ..., 0.26055628, 0.26055628,
              0.26055628],
             [0.27413238, 0.27413238, 0.27413238, ..., 0.27413238, 0.27413238,
              0.27413238]])

    • smallest_eigval
      (chain, draw)
      float64
      nan nan nan nan ... nan nan nan nan

      array([[nan, nan, nan, ..., nan, nan, nan],
             [nan, nan, nan, ..., nan, nan, nan],
             [nan, nan, nan, ..., nan, nan, nan],
             [nan, nan, nan, ..., nan, nan, nan]])

    • energy_error
      (chain, draw)
      float64
      0.1063 -0.1922 ... 0.6039 -0.8926

      array([[ 0.10633161, -0.19223807, -0.07324313, ..., -0.05689863,
               0.11804534,  0.04478887],
             [-0.11199666,  0.20578808, -0.1399356 , ...,  0.205265  ,
              -0.25117668,  1.01038826],
             [-0.13750741, -0.03513089,  0.20506484, ..., -0.70430077,
              -0.01280797, -0.16463478],
             [-0.1666122 ,  0.61632692, -0.48263151, ...,  0.10197503,
               0.60388915, -0.89258914]])

    • diverging
      (chain, draw)
      bool
      False False False ... False False

      array([[False, False, False, ..., False, False, False],
             [False, False, False, ..., False, False, False],
             [False, False, False, ..., False, False, False],
             [False, False, False, ..., False, False, False]])

    • index_in_trajectory
      (chain, draw)
      int64
      8 -6 -6 -6 10 ... -12 10 10 -10 -6

      array([[  8,  -6,  -6, ...,   7, -11, -10],
             [-15,  15,   9, ...,  12,   8,   4],
             [-14,   6, -12, ..., -13,   7,  -6],
             [  3,   6,   2, ...,  10, -10,  -6]])

    • energy
      (chain, draw)
      float64
      -186.7 -183.7 ... -182.6 -182.3

      array([[-186.71221527, -183.69718813, -180.80066873, ..., -187.0691717 ,
              -185.80251922, -185.85593343],
             [-186.62691362, -183.68157888, -180.83446734, ..., -180.21656638,
              -177.21042455, -175.34992831],
             [-185.6449068 , -189.74583709, -186.80186591, ..., -176.16387582,
              -182.34563041, -179.97120628],
             [-187.09037814, -183.89547442, -175.47726337, ..., -188.01409915,
              -182.5587388 , -182.28892311]])

    • process_time_diff
      (chain, draw)
      float64
      0.007787 0.01354 ... 0.01025

      array([[0.007787, 0.013544, 0.01156 , ..., 0.00884 , 0.010774, 0.009   ],
             [0.010579, 0.011096, 0.009645, ..., 0.007559, 0.010655, 0.012674],
             [0.015694, 0.01198 , 0.01068 , ..., 0.009102, 0.008428, 0.009367],
             [0.013038, 0.014209, 0.010028, ..., 0.012215, 0.008676, 0.010252]])

    • reached_max_treedepth
      (chain, draw)
      bool
      False False False ... False False

      array([[False, False, False, ..., False, False, False],
             [False, False, False, ..., False, False, False],
             [False, False, False, ..., False, False, False],
             [False, False, False, ..., False, False, False]])

  • Indexes: (2)
    • chain
      PandasIndex

      PandasIndex(Int64Index([0, 1, 2, 3], dtype='int64', name='chain'))

    • draw
      PandasIndex

      PandasIndex(Int64Index([   0,    1,    2,    3,    4,    5,    6,    7,    8,    9,
                  ...
                  1990, 1991, 1992, 1993, 1994, 1995, 1996, 1997, 1998, 1999],
                 dtype='int64', name='draw', length=2000))

  • Attributes: (6)

    created_at :

    2023-02-21T19:21:22.951462

    arviz_version :

    0.14.0

    inference_library :

    pymc

    inference_library_version :

    5.0.1

    sampling_time :

    36.195340156555176

    tuning_steps :

    1000

  
  
• prior

  <xarray.Dataset>
  Dimensions:                (chain: 1, draw: 500, equations: 2,
                              noise_chol_corr_dim_0: 2, noise_chol_corr_dim_1: 2,
                              noise_chol_stds_dim_0: 2, time: 49, betaX_dim_1: 2,
                              noise_chol_dim_0: 3, lags: 2, cross_vars: 2)
  Coordinates:
    * chain                  (chain) int64 0
    * draw                   (draw) int64 0 1 2 3 4 5 ... 494 495 496 497 498 499
    * equations              (equations) <U7 'dl_gdp' 'dl_cons'
    * noise_chol_corr_dim_0  (noise_chol_corr_dim_0) int64 0 1
    * noise_chol_corr_dim_1  (noise_chol_corr_dim_1) int64 0 1
    * noise_chol_stds_dim_0  (noise_chol_stds_dim_0) int64 0 1
    * time                   (time) int64 2 3 4 5 6 7 8 9 ... 44 45 46 47 48 49 50
    * betaX_dim_1            (betaX_dim_1) int64 0 1
    * noise_chol_dim_0       (noise_chol_dim_0) int64 0 1 2
    * lags                   (lags) int64 1 2
    * cross_vars             (cross_vars) <U7 'dl_gdp' 'dl_cons'
  Data variables:
      alpha                  (chain, draw, equations) float64 -0.02173 ... 0.04148
      noise_chol_corr        (chain, draw, noise_chol_corr_dim_0, noise_chol_corr_dim_1) float64 ...
      noise_chol_stds        (chain, draw, noise_chol_stds_dim_0) float64 0.479...
      betaX                  (chain, draw, time, betaX_dim_1) float64 0.05801 ....
      noise_chol             (chain, draw, noise_chol_dim_0) float64 0.4793 ......
      lag_coefs              (chain, draw, equations, lags, cross_vars) float64 ...
  Attributes:
      created_at:                 2023-02-21T19:20:42.612680
      arviz_version:              0.14.0
      inference_library:          pymc
      inference_library_version:  5.0.1

  xarray.Dataset

  • Dimensions:
    • chain: 1
    • draw: 500
    • equations: 2
    • noise_chol_corr_dim_0: 2
    • noise_chol_corr_dim_1: 2
    • noise_chol_stds_dim_0: 2
    • time: 49
    • betaX_dim_1: 2
    • noise_chol_dim_0: 3
    • lags: 2
    • cross_vars: 2
  • Coordinates: (11)
    • chain
      (chain)
      int64
      0

      array([0])

    • draw
      (draw)
      int64
      0 1 2 3 4 5 ... 495 496 497 498 499

      array([  0,   1,   2, ..., 497, 498, 499])

    • equations
      (equations)
      <U7
      'dl_gdp' 'dl_cons'

      array(['dl_gdp', 'dl_cons'], dtype='<U7')

    • noise_chol_corr_dim_0
      (noise_chol_corr_dim_0)
      int64
      0 1

      array([0, 1])

    • noise_chol_corr_dim_1
      (noise_chol_corr_dim_1)
      int64
      0 1

      array([0, 1])

    • noise_chol_stds_dim_0
      (noise_chol_stds_dim_0)
      int64
      0 1

      array([0, 1])

    • time
      (time)
      int64
      2 3 4 5 6 7 8 ... 45 46 47 48 49 50

      array([ 2,  3,  4,  5,  6,  7,  8,  9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19,
             20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37,
             38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50])

    • betaX_dim_1
      (betaX_dim_1)
      int64
      0 1

      array([0, 1])

    • noise_chol_dim_0
      (noise_chol_dim_0)
      int64
      0 1 2

      array([0, 1, 2])

    • lags
      (lags)
      int64
      1 2

      array([1, 2])

    • cross_vars
      (cross_vars)
      <U7
      'dl_gdp' 'dl_cons'

      array(['dl_gdp', 'dl_cons'], dtype='<U7')

  • Data variables: (6)
    • alpha
      (chain, draw, equations)
      float64
      -0.02173 -0.1333 ... 0.04148

      array([[[-2.17321208e-02, -1.33334684e-01],
              [ 5.34931179e-02,  1.59499447e-01],
              [-9.49314248e-03,  5.64533641e-02],
              [-2.33126640e-02, -1.02705798e-01],
              [ 1.26733115e-01,  7.69344011e-02],
              [-1.80317474e-02,  6.57613825e-02],
              [-1.13071369e-01,  1.51406968e-01],
              [-1.54448261e-01,  1.31782276e-01],
              [-3.17081453e-02,  1.90268718e-02],
              [-1.18113054e-01,  1.62388440e-01],
              [ 7.05559903e-02, -1.19139213e-02],
              [ 1.33057457e-01, -3.39059486e-02],
              [-2.55956804e-02, -6.54044042e-02],
              [-8.17956874e-03,  1.98647714e-01],
              [ 5.57149931e-03, -4.32720912e-02],
              [ 8.87368333e-02,  1.71219288e-01],
              [ 2.10682139e-02, -1.24616571e-01],
              [-1.20201764e-03, -1.17523975e-01],
              [-9.64406169e-02,  6.16024940e-02],
              [ 8.76603291e-02, -8.72035128e-02],
      ...
              [ 1.37657923e-01,  1.27996799e-01],
              [ 5.13551369e-02, -1.31544671e-01],
              [ 1.00260415e-02, -1.07408884e-03],
              [-5.83019260e-02, -2.54488291e-02],
              [ 3.70272843e-02,  2.20626431e-01],
              [ 3.03187875e-02,  2.52427570e-02],
              [ 7.58630825e-02, -2.94336306e-01],
              [-2.36982827e-02, -8.84849345e-03],
              [-1.77442781e-02, -8.50522727e-03],
              [ 4.80910337e-02,  1.46007292e-02],
              [ 1.67488753e-01,  2.23774479e-01],
              [-4.09985360e-02, -1.48536396e-02],
              [ 4.67375840e-02, -2.03043589e-02],
              [-1.12377222e-01, -8.82438720e-02],
              [-9.90900254e-02,  1.36751395e-01],
              [-2.53327369e-02, -7.34878400e-02],
              [-4.96505019e-02,  8.64545788e-02],
              [ 3.48784048e-02,  2.66594474e-01],
              [ 2.83293109e-02, -7.74836476e-02],
              [ 7.36847485e-02,  4.14770386e-02]]])

    • noise_chol_corr
      (chain, draw, noise_chol_corr_dim_0, noise_chol_corr_dim_1)
      float64
      1.0 -0.2284 -0.2284 ... -0.5198 1.0

      array([[[[ 1.        , -0.22837651],
               [-0.22837651,  1.        ]],
      
              [[ 1.        ,  0.82351754],
               [ 0.82351754,  1.        ]],
      
              [[ 1.        ,  0.34327501],
               [ 0.34327501,  1.        ]],
      
              ...,
      
              [[ 1.        ,  0.69452847],
               [ 0.69452847,  1.        ]],
      
              [[ 1.        ,  0.42945802],
               [ 0.42945802,  1.        ]],
      
              [[ 1.        , -0.5198015 ],
               [-0.5198015 ,  1.        ]]]])

    • noise_chol_stds
      (chain, draw, noise_chol_stds_dim_0)
      float64
      0.4793 1.124 ... 0.01728 0.2597

      array([[[4.79284896e-01, 1.12391550e+00],
              [6.97040739e-01, 9.54652181e-01],
              [1.59097130e+00, 3.31920295e-01],
              [1.15243377e+00, 7.82453571e-02],
              [5.53414777e-01, 2.06989481e-01],
              [2.14023145e+00, 4.47391867e-02],
              [2.60874906e-01, 1.49356985e+00],
              [1.20751677e+00, 5.06368239e-01],
              [2.93252219e-01, 9.22195628e-02],
              [5.59250055e-01, 8.46677717e-01],
              [3.33437205e-01, 5.50176517e-01],
              [1.67605175e-02, 3.56294802e-01],
              [2.30751158e-01, 1.10548076e+00],
              [1.55569836e+00, 9.90290581e-01],
              [1.41325046e+00, 1.01313301e+00],
              [7.50295560e-01, 6.17414964e-01],
              [5.22344641e-01, 7.23205322e-01],
              [1.41627088e+00, 8.49720046e-01],
              [1.80338965e+00, 1.65866311e+00],
              [3.62065401e-02, 3.03571965e+00],
      ...
              [1.51141877e+00, 1.44833737e+00],
              [1.10143071e-01, 4.36921244e-01],
              [1.53377987e+00, 8.92707864e-01],
              [7.70254088e-01, 2.15079477e+00],
              [1.24557997e-01, 1.00007158e+00],
              [1.26361991e+00, 1.12878392e-01],
              [2.11441792e-01, 6.76319368e-02],
              [7.25305848e-01, 2.20809866e+00],
              [2.95885724e-01, 1.33235181e+00],
              [9.91874436e-01, 9.99117482e-01],
              [9.37832970e-01, 8.39861991e-01],
              [1.54576189e-01, 2.57803495e-01],
              [1.05339644e+00, 2.84286425e-01],
              [1.87852079e-01, 6.49825798e-01],
              [1.41159170e-01, 2.71423310e-01],
              [1.58019583e+00, 1.23724822e+00],
              [8.82855209e-01, 2.96738277e+00],
              [3.47493609e-01, 2.50978228e+00],
              [1.11940315e+00, 6.25613502e-01],
              [1.72818848e-02, 2.59731360e-01]]])

    • betaX
      (chain, draw, time, betaX_dim_1)
      float64
      0.05801 0.1928 ... 0.1824 0.1416

      array([[[[ 0.05801452,  0.19282852],
               [ 0.06136907,  0.19021009],
               [ 0.06498837,  0.12662961],
               ...,
               [ 0.1263401 ,  0.22265808],
               [ 0.09465621,  0.1605613 ],
               [ 0.12072331,  0.0342081 ]],
      
              [[ 0.03458694,  0.04445992],
               [ 0.077954  ,  0.03533871],
               [ 0.01711512,  0.03041004],
               ...,
               [ 0.09682593,  0.02314592],
               [ 0.09850186,  0.01292326],
               [-0.03044917, -0.00261849]],
      
              [[ 0.03363234,  0.0448288 ],
               [ 0.0509058 ,  0.01335756],
               [ 0.0114371 , -0.01758728],
               ...,
      ...
               ...,
               [-0.03846538,  0.06103218],
               [-0.03609514,  0.01253422],
               [ 0.11130663,  0.03136471]],
      
              [[ 0.15524741,  0.02883929],
               [ 0.16256085,  0.05265778],
               [ 0.12545039, -0.00345506],
               ...,
               [ 0.14048099,  0.04771948],
               [ 0.11854582,  0.04748313],
               [ 0.01834497, -0.07335791]],
      
              [[ 0.13089945, -0.05260524],
               [ 0.15576556, -0.06532189],
               [ 0.20108248, -0.01115042],
               ...,
               [ 0.12102344,  0.0121013 ],
               [ 0.13921009, -0.00432658],
               [ 0.18239744,  0.14157838]]]])

    • noise_chol
      (chain, draw, noise_chol_dim_0)
      float64
      0.4793 -0.2567 ... -0.135 0.2219

      array([[[ 0.4792849 , -0.2566759 ,  1.09421366],
              [ 0.69704074,  0.78617282,  0.5415654 ],
              [ 1.5909713 ,  0.11393994,  0.31175114],
              ...,
              [ 0.34749361,  1.74311526,  1.80570106],
              [ 1.11940315,  0.26867474,  0.56498331],
              [ 0.01728188, -0.13500875,  0.22188514]]])

    • lag_coefs
      (chain, draw, equations, lags, cross_vars)
      float64
      0.8718 -0.5211 ... 0.5638 -0.01947

      array([[[[[ 0.87178822, -0.52109414],
                [ 0.81192969,  0.10257338]],
      
               [[ 1.66388457,  1.39492785],
                [ 0.2402051 ,  0.0541874 ]]],
      
      
              [[[-0.30618212,  0.79757413],
                [ 1.30337738, -0.79747345]],
      
               [[ 0.38143198,  0.35600826],
                [-0.37832199,  0.309069  ]]],
      
      
              [[[-0.2397557 ,  0.95264081],
                [ 0.11852561, -0.19028039]],
      
               [[ 0.88990685,  0.74043063],
                [-0.60850236, -0.71937965]]],
      
      ...
      
              [[[-0.33751836, -2.02597956],
                [ 1.06725697, -0.69540281]],
      
               [[ 1.2472135 ,  0.17422232],
                [-0.62668472, -0.00886019]]],
      
      
              [[[ 0.89838374,  1.17917942],
                [-0.07513856,  0.81314769]],
      
               [[-0.23967996,  1.03413277],
                [ 0.52659114, -0.71997653]]],
      
      
              [[[ 0.5282788 , -0.52010047],
                [ 0.32594737,  2.63132424]],
      
               [[ 0.40303183, -1.73076034],
                [ 0.56375655, -0.01946577]]]]])

  • Indexes: (11)
    • chain
      PandasIndex

      PandasIndex(Int64Index([0], dtype='int64', name='chain'))

    • draw
      PandasIndex

      PandasIndex(Int64Index([  0,   1,   2,   3,   4,   5,   6,   7,   8,   9,
                  ...
                  490, 491, 492, 493, 494, 495, 496, 497, 498, 499],
                 dtype='int64', name='draw', length=500))

    • equations
      PandasIndex

      PandasIndex(Index(['dl_gdp', 'dl_cons'], dtype='object', name='equations'))

    • noise_chol_corr_dim_0
      PandasIndex

      PandasIndex(Int64Index([0, 1], dtype='int64', name='noise_chol_corr_dim_0'))

    • noise_chol_corr_dim_1
      PandasIndex

      PandasIndex(Int64Index([0, 1], dtype='int64', name='noise_chol_corr_dim_1'))

    • noise_chol_stds_dim_0
      PandasIndex

      PandasIndex(Int64Index([0, 1], dtype='int64', name='noise_chol_stds_dim_0'))

    • time
      PandasIndex

      PandasIndex(Int64Index([ 2,  3,  4,  5,  6,  7,  8,  9, 10, 11, 12, 13, 14, 15, 16, 17, 18,
                  19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35,
                  36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50],
                 dtype='int64', name='time'))

    • betaX_dim_1
      PandasIndex

      PandasIndex(Int64Index([0, 1], dtype='int64', name='betaX_dim_1'))

    • noise_chol_dim_0
      PandasIndex

      PandasIndex(Int64Index([0, 1, 2], dtype='int64', name='noise_chol_dim_0'))

    • lags
      PandasIndex

      PandasIndex(Int64Index([1, 2], dtype='int64', name='lags'))

    • cross_vars
      PandasIndex

      PandasIndex(Index(['dl_gdp', 'dl_cons'], dtype='object', name='cross_vars'))

  • Attributes: (4)

    created_at :

    2023-02-21T19:20:42.612680

    arviz_version :

    0.14.0

    inference_library :

    pymc

    inference_library_version :

    5.0.1

  
  
• prior_predictive

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    * equations  (equations) <U7 'dl_gdp' 'dl_cons'
  Data variables:
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      arviz_version:              0.14.0
      inference_library:          pymc
      inference_library_version:  5.0.1

  xarray.Dataset

  • Dimensions:
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    • equations
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  • Data variables: (1)
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      (chain, draw, time, equations)
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      PandasIndex

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    • time
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    • equations
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    created_at :

    2023-02-21T19:20:42.614050

    arviz_version :

    0.14.0

    inference_library :

    pymc

    inference_library_version :

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• observed_data

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  Dimensions:    (time: 49, equations: 2)
  Coordinates:
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    * equations  (equations) <U7 'dl_gdp' 'dl_cons'
  Data variables:
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  Attributes:
      created_at:                 2023-02-21T19:20:42.614347
      arviz_version:              0.14.0
      inference_library:          pymc
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  xarray.Dataset

  • Dimensions:
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    • equations: 2
  • Coordinates: (2)
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      (time)
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    • equations
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  • Data variables: (1)
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             [ 0.08127144,  0.02305265],
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      ...
             [ 0.05728948,  0.04324766],
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             [ 0.06565545,  0.03202102],
             [ 0.05577724,  0.06123691],
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             [ 0.01739857, -0.01160896],
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             [-0.00052368, -0.017138  ],
             [ 0.01259055, -0.00163944],
             [ 0.08354761,  0.02976708],
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    • time
      PandasIndex

      PandasIndex(Int64Index([ 2,  3,  4,  5,  6,  7,  8,  9, 10, 11, 12, 13, 14, 15, 16, 17, 18,
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                  36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50],
                 dtype='int64', name='time'))

    • equations
      PandasIndex

      PandasIndex(Index(['dl_gdp', 'dl_cons'], dtype='object', name='equations'))

  • Attributes: (4)

    created_at :

    2023-02-21T19:20:42.614347

    arviz_version :

    0.14.0

    inference_library :

    pymc

    inference_library_version :

    5.0.1

  
  
• constant_data

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  Dimensions:    (time: 49, equations: 2)
  Coordinates:
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    * equations  (equations) <U7 'dl_gdp' 'dl_cons'
  Data variables:
      data_obs   (time, equations) float64 0.04613 0.06834 ... 0.1264 0.05461
  Attributes:
      created_at:                 2023-02-21T19:20:42.614628
      arviz_version:              0.14.0
      inference_library:          pymc
      inference_library_version:  5.0.1

  xarray.Dataset

  • Dimensions:
    • time: 49
    • equations: 2
  • Coordinates: (2)
    • time
      (time)
      int64
      2 3 4 5 6 7 8 ... 45 46 47 48 49 50

      array([ 2,  3,  4,  5,  6,  7,  8,  9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19,
             20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37,
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    • equations
      (equations)
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      array(['dl_gdp', 'dl_cons'], dtype='<U7')

  • Data variables: (1)
    • data_obs
      (time, equations)
      float64
      0.04613 0.06834 ... 0.1264 0.05461

      array([[ 0.04613358,  0.06834012],
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             [ 0.08127144,  0.02305265],
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             [ 0.05728948,  0.04324766],
             [ 0.02965185,  0.02806114],
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             [ 0.05577724,  0.06123691],
             [ 0.04860445,  0.05797527],
             [ 0.05169516,  0.06437874],
             [-0.04590363,  0.00356559],
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             [ 0.01739857, -0.01160896],
             [ 0.01062858,  0.00262455],
             [-0.00052368, -0.017138  ],
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             [ 0.08354761,  0.02976708],
             [ 0.22455252,  0.02970416],
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  • Indexes: (2)
    • time
      PandasIndex

      PandasIndex(Int64Index([ 2,  3,  4,  5,  6,  7,  8,  9, 10, 11, 12, 13, 14, 15, 16, 17, 18,
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    • equations
      PandasIndex

      PandasIndex(Index(['dl_gdp', 'dl_cons'], dtype='object', name='equations'))

  • Attributes: (4)

    created_at :

    2023-02-21T19:20:42.614628

    arviz_version :

    0.14.0

    inference_library :

    pymc

    inference_library_version :

    5.0.1

  
  

az.plot_trace(idata_ireland, var_names=["lag_coefs", "alpha", "betaX"], kind="rank_vlines");

def plot_ppc_macro(idata, df, group="posterior_predictive"):
    df = pd.DataFrame(idata["observed_data"]["obs"].data, columns=["dl_gdp", "dl_cons"])
    fig, axs = plt.subplots(2, 1, figsize=(20, 10))
    axs = axs.flatten()
    ppc = az.extract(idata, group=group, num_samples=100)["obs"]

    shade_background(ppc, axs, 0, "inferno")
    axs[0].plot(np.arange(ppc.shape[0]), ppc[:, 0, :].mean(axis=1), color="cyan", label="Mean")
    axs[0].plot(df["dl_gdp"], "o", mfc="black", mec="white", mew=1, markersize=7, label="Observed")
    axs[0].set_title("Differenced and Logged GDP")
    axs[0].legend()
    shade_background(ppc, axs, 1, "inferno")
    axs[1].plot(df["dl_cons"], "o", mfc="black", mec="white", mew=1, markersize=7, label="Observed")
    axs[1].plot(np.arange(ppc.shape[0]), ppc[:, 1, :].mean(axis=1), color="cyan", label="Mean")
    axs[1].set_title("Differenced and Logged Consumption")
    axs[1].legend()


plot_ppc_macro(idata_ireland, ireland_df)

ax = az.plot_posterior(
    idata_ireland,
    var_names="noise_chol_corr",
    hdi_prob="hide",
    point_estimate="mean",
    grid=(2, 2),
    kind="hist",
    ec="black",
    figsize=(10, 6),
)

Comparison with Statsmodels

It's worthwhile comparing these model fits to the one achieved by Statsmodels just to see if we can recover a similar story.

VAR_model = sm.tsa.VAR(ireland_df[["dl_gdp", "dl_cons"]])
results = VAR_model.fit(2, trend="c")

results.params

	dl_gdp	dl_cons
const	0.034145	0.006996
L1.dl_gdp	0.324904	0.330003
L1.dl_cons	0.076629	0.305824
L2.dl_gdp	0.137721	-0.053677
L2.dl_cons	-0.278745	0.033728

The intercept parameters broadly agree with our Bayesian model with some differences in the implied relationships defined by the estimates for the lagged terms.

corr = pd.DataFrame(results.resid_corr, columns=["dl_gdp", "dl_cons"])
corr.index = ["dl_gdp", "dl_cons"]
corr

	dl_gdp	dl_cons
dl_gdp	1.000000	0.435807
dl_cons	0.435807	1.000000

The residual correlation estimates reported by statsmodels agree quite closely with the multivariate gaussian correlation between the variables in our Bayesian model.

az.summary(idata_ireland, var_names=["alpha", "lag_coefs", "noise_chol_corr"])

/Users/nathanielforde/mambaforge/envs/myjlabenv/lib/python3.11/site-packages/arviz/stats/diagnostics.py:584: RuntimeWarning: invalid value encountered in scalar divide
  (between_chain_variance / within_chain_variance + num_samples - 1) / (num_samples)

	mean	sd	hdi_3%	hdi_97%	mcse_mean	mcse_sd	ess_bulk	ess_tail	r_hat
alpha[dl_gdp]	0.033	0.011	0.012	0.053	0.000	0.000	6683.0	5919.0	1.0
alpha[dl_cons]	0.007	0.007	-0.007	0.020	0.000	0.000	7651.0	5999.0	1.0
lag_coefs[dl_gdp, 1, dl_gdp]	0.321	0.170	0.008	0.642	0.002	0.002	6984.0	6198.0	1.0
lag_coefs[dl_gdp, 1, dl_cons]	0.071	0.273	-0.447	0.582	0.003	0.003	7376.0	5466.0	1.0
lag_coefs[dl_gdp, 2, dl_gdp]	0.133	0.190	-0.228	0.488	0.002	0.002	7471.0	6128.0	1.0
lag_coefs[dl_gdp, 2, dl_cons]	-0.235	0.269	-0.748	0.259	0.003	0.002	8085.0	5963.0	1.0
lag_coefs[dl_cons, 1, dl_gdp]	0.331	0.106	0.133	0.528	0.001	0.001	7670.0	6360.0	1.0
lag_coefs[dl_cons, 1, dl_cons]	0.302	0.170	-0.012	0.616	0.002	0.001	7963.0	6150.0	1.0
lag_coefs[dl_cons, 2, dl_gdp]	-0.054	0.118	-0.279	0.163	0.001	0.001	8427.0	6296.0	1.0
lag_coefs[dl_cons, 2, dl_cons]	0.048	0.170	-0.259	0.378	0.002	0.002	8669.0	6264.0	1.0
noise_chol_corr[0, 0]	1.000	0.000	1.000	1.000	0.000	0.000	8000.0	8000.0	NaN
noise_chol_corr[0, 1]	0.416	0.123	0.180	0.633	0.001	0.001	9155.0	6052.0	1.0
noise_chol_corr[1, 0]	0.416	0.123	0.180	0.633	0.001	0.001	9155.0	6052.0	1.0
noise_chol_corr[1, 1]	1.000	0.000	1.000	1.000	0.000	0.000	7871.0	8000.0	1.0

We plot the alpha parameter estimates against the Statsmodels estimates

az.plot_posterior(idata_ireland, var_names=["alpha"], ref_val=[0.034145, 0.006996]);

az.plot_posterior(
    idata_ireland,
    var_names=["lag_coefs"],
    ref_val=[0.330003, -0.053677],
    coords={"equations": "dl_cons", "lags": [1, 2], "cross_vars": "dl_gdp"},
);

We can see here again how the Bayesian VAR model recovers much of the same story. Similar magnitudes in the estimates for the alpha terms for both equations and a clear relationship between the first lagged GDP numbers and consumption along with a very similar covariance structure.

Adding a Bayesian Twist: Hierarchical VARs

In addition we can add some hierarchical parameters if we want to model multiple countries and the relationship between these economic metrics at the national level. This is a useful technique in the cases where we have reasonably short timeseries data because it allows us to "borrow" information across the countries to inform the estimates of the key parameters.

def make_hierarchical_model(n_lags, n_eqs, df, group_field, prior_checks=True):
    cols = [col for col in df.columns if col != group_field]
    coords = {"lags": np.arange(n_lags) + 1, "equations": cols, "cross_vars": cols}

    groups = df[group_field].unique()

    with pm.Model(coords=coords) as model:
        ## Hierarchical Priors
        rho = pm.Beta("rho", alpha=2, beta=2)
        alpha_hat_location = pm.Normal("alpha_hat_location", 0, 0.1)
        alpha_hat_scale = pm.InverseGamma("alpha_hat_scale", 3, 0.5)
        beta_hat_location = pm.Normal("beta_hat_location", 0, 0.1)
        beta_hat_scale = pm.InverseGamma("beta_hat_scale", 3, 0.5)
        omega_global, _, _ = pm.LKJCholeskyCov(
            "omega_global", n=n_eqs, eta=1.0, sd_dist=pm.Exponential.dist(1)
        )

        for grp in groups:
            df_grp = df[df[group_field] == grp][cols]
            z_scale_beta = pm.InverseGamma(f"z_scale_beta_{grp}", 3, 0.5)
            z_scale_alpha = pm.InverseGamma(f"z_scale_alpha_{grp}", 3, 0.5)
            lag_coefs = pm.Normal(
                f"lag_coefs_{grp}",
                mu=beta_hat_location,
                sigma=beta_hat_scale * z_scale_beta,
                dims=["equations", "lags", "cross_vars"],
            )
            alpha = pm.Normal(
                f"alpha_{grp}",
                mu=alpha_hat_location,
                sigma=alpha_hat_scale * z_scale_alpha,
                dims=("equations",),
            )

            betaX = calc_ar_step(lag_coefs, n_eqs, n_lags, df_grp)
            betaX = pm.Deterministic(f"betaX_{grp}", betaX)
            mean = alpha + betaX

            n = df_grp.shape[1]
            noise_chol, _, _ = pm.LKJCholeskyCov(
                f"noise_chol_{grp}", eta=10, n=n, sd_dist=pm.Exponential.dist(1)
            )
            omega = pm.Deterministic(f"omega_{grp}", rho * omega_global + (1 - rho) * noise_chol)
            obs = pm.MvNormal(f"obs_{grp}", mu=mean, chol=omega, observed=df_grp.values[n_lags:])

        if prior_checks:
            idata = pm.sample_prior_predictive()
            return model, idata
        else:
            idata = pm.sample_prior_predictive()
            idata.extend(sample_blackjax_nuts(2000, random_seed=120))
            pm.sample_posterior_predictive(idata, extend_inferencedata=True)
    return model, idata

The model design allows for a non-centred parameterisation of the key likeihood for each of the individual country components by allowing the us to shift the country specific estimates away from the hierarchical mean. This is done by rho * omega_global + (1 - rho) * noise_chol line. The parameter rho determines the share of impact each country's data contributes to the estimation of the covariance relationship among the economic variables. Similar country specific adjustments are made with the z_alpha_scale and z_beta_scale parameters.

df_final = gdp_hierarchical[["country", "dl_gdp", "dl_cons", "dl_gfcf"]]
model_full_test, idata_full_test = make_hierarchical_model(
    2,
    3,
    df_final,
    "country",
    prior_checks=False,
)

Sampling: [alpha_Australia, alpha_Canada, alpha_Chile, alpha_Ireland, alpha_New Zealand, alpha_South Africa, alpha_United Kingdom, alpha_United States, alpha_hat_location, alpha_hat_scale, beta_hat_location, beta_hat_scale, lag_coefs_Australia, lag_coefs_Canada, lag_coefs_Chile, lag_coefs_Ireland, lag_coefs_New Zealand, lag_coefs_South Africa, lag_coefs_United Kingdom, lag_coefs_United States, noise_chol_Australia, noise_chol_Canada, noise_chol_Chile, noise_chol_Ireland, noise_chol_New Zealand, noise_chol_South Africa, noise_chol_United Kingdom, noise_chol_United States, obs_Australia, obs_Canada, obs_Chile, obs_Ireland, obs_New Zealand, obs_South Africa, obs_United Kingdom, obs_United States, omega_global, rho, z_scale_alpha_Australia, z_scale_alpha_Canada, z_scale_alpha_Chile, z_scale_alpha_Ireland, z_scale_alpha_New Zealand, z_scale_alpha_South Africa, z_scale_alpha_United Kingdom, z_scale_alpha_United States, z_scale_beta_Australia, z_scale_beta_Canada, z_scale_beta_Chile, z_scale_beta_Ireland, z_scale_beta_New Zealand, z_scale_beta_South Africa, z_scale_beta_United Kingdom, z_scale_beta_United States]

Compiling...
Compilation time =  0:00:12.203665
Sampling...
Sampling time =  0:01:13.331452
Transforming variables...
Transformation time =  0:00:13.215405

Sampling: [obs_Australia, obs_Canada, obs_Chile, obs_Ireland, obs_New Zealand, obs_South Africa, obs_United Kingdom, obs_United States]

100.00% [8000/8000 07:19<00:00]

idata_full_test

arviz.InferenceData

• posterior

  <xarray.Dataset>
  Dimensions:                               (chain: 4, draw: 2000, equations: 3,
                                             lags: 2, cross_vars: 3,
                                             omega_global_dim_0: 6,
                                             noise_chol_Australia_dim_0: 6,
                                             noise_chol_Canada_dim_0: 6,
                                             noise_chol_Chile_dim_0: 6,
                                             ...
                                             betaX_United States_dim_1: 3,
                                             noise_chol_United States_corr_dim_0: 3,
                                             noise_chol_United States_corr_dim_1: 3,
                                             noise_chol_United States_stds_dim_0: 3,
                                             omega_United States_dim_0: 3,
                                             omega_United States_dim_1: 3)
  Coordinates: (12/73)
    * chain                                 (chain) int64 0 1 2 3
    * draw                                  (draw) int64 0 1 2 ... 1997 1998 1999
    * equations                             (equations) <U7 'dl_gdp' ... 'dl_gfcf'
    * lags                                  (lags) int64 1 2
    * cross_vars                            (cross_vars) <U7 'dl_gdp' ... 'dl_g...
    * omega_global_dim_0                    (omega_global_dim_0) int64 0 1 2 3 4 5
      ...                                    ...
    * betaX_United States_dim_1             (betaX_United States_dim_1) int64 0...
    * noise_chol_United States_corr_dim_0   (noise_chol_United States_corr_dim_0) int64 ...
    * noise_chol_United States_corr_dim_1   (noise_chol_United States_corr_dim_1) int64 ...
    * noise_chol_United States_stds_dim_0   (noise_chol_United States_stds_dim_0) int64 ...
    * omega_United States_dim_0             (omega_United States_dim_0) int64 0...
    * omega_United States_dim_1             (omega_United States_dim_1) int64 0...
  Data variables: (12/80)
      alpha_hat_location                    (chain, draw) float64 0.01867 ... 0...
      beta_hat_location                     (chain, draw) float64 0.03707 ... 0...
      lag_coefs_Australia                   (chain, draw, equations, lags, cross_vars) float64 ...
      alpha_Australia                       (chain, draw, equations) float64 0....
      lag_coefs_Canada                      (chain, draw, equations, lags, cross_vars) float64 ...
      alpha_Canada                          (chain, draw, equations) float64 0....
      ...                                    ...
      noise_chol_United Kingdom_stds        (chain, draw, noise_chol_United Kingdom_stds_dim_0) float64 ...
      omega_United Kingdom                  (chain, draw, omega_United Kingdom_dim_0, omega_United Kingdom_dim_1) float64 ...
      betaX_United States                   (chain, draw, betaX_United States_dim_0, betaX_United States_dim_1) float64 ...
      noise_chol_United States_corr         (chain, draw, noise_chol_United States_corr_dim_0, noise_chol_United States_corr_dim_1) float64 ...
      noise_chol_United States_stds         (chain, draw, noise_chol_United States_stds_dim_0) float64 ...
      omega_United States                   (chain, draw, omega_United States_dim_0, omega_United States_dim_1) float64 ...
  Attributes:
      created_at:     2023-02-21T19:24:14.259388
      arviz_version:  0.14.0

  xarray.Dataset

  • Dimensions:
    • chain: 4
    • draw: 2000
    • equations: 3
    • lags: 2
    • cross_vars: 3
    • omega_global_dim_0: 6
    • noise_chol_Australia_dim_0: 6
    • noise_chol_Canada_dim_0: 6
    • noise_chol_Chile_dim_0: 6
    • noise_chol_Ireland_dim_0: 6
    • noise_chol_New Zealand_dim_0: 6
    • noise_chol_South Africa_dim_0: 6
    • noise_chol_United Kingdom_dim_0: 6
    • noise_chol_United States_dim_0: 6
    • omega_global_corr_dim_0: 3
    • omega_global_corr_dim_1: 3
    • omega_global_stds_dim_0: 3
    • betaX_Australia_dim_0: 49
    • betaX_Australia_dim_1: 3
    • noise_chol_Australia_corr_dim_0: 3
    • noise_chol_Australia_corr_dim_1: 3
    • noise_chol_Australia_stds_dim_0: 3
    • omega_Australia_dim_0: 3
    • omega_Australia_dim_1: 3
    • betaX_Canada_dim_0: 22
    • betaX_Canada_dim_1: 3
    • noise_chol_Canada_corr_dim_0: 3
    • noise_chol_Canada_corr_dim_1: 3
    • noise_chol_Canada_stds_dim_0: 3
    • omega_Canada_dim_0: 3
    • omega_Canada_dim_1: 3
    • betaX_Chile_dim_0: 49
    • betaX_Chile_dim_1: 3
    • noise_chol_Chile_corr_dim_0: 3
    • noise_chol_Chile_corr_dim_1: 3
    • noise_chol_Chile_stds_dim_0: 3
    • omega_Chile_dim_0: 3
    • omega_Chile_dim_1: 3
    • betaX_Ireland_dim_0: 49
    • betaX_Ireland_dim_1: 3
    • noise_chol_Ireland_corr_dim_0: 3
    • noise_chol_Ireland_corr_dim_1: 3
    • noise_chol_Ireland_stds_dim_0: 3
    • omega_Ireland_dim_0: 3
    • omega_Ireland_dim_1: 3
    • betaX_New Zealand_dim_0: 41
    • betaX_New Zealand_dim_1: 3
    • noise_chol_New Zealand_corr_dim_0: 3
    • noise_chol_New Zealand_corr_dim_1: 3
    • noise_chol_New Zealand_stds_dim_0: 3
    • omega_New Zealand_dim_0: 3
    • omega_New Zealand_dim_1: 3
    • betaX_South Africa_dim_0: 49
    • betaX_South Africa_dim_1: 3
    • noise_chol_South Africa_corr_dim_0: 3
    • noise_chol_South Africa_corr_dim_1: 3
    • noise_chol_South Africa_stds_dim_0: 3
    • omega_South Africa_dim_0: 3
    • omega_South Africa_dim_1: 3
    • betaX_United Kingdom_dim_0: 49
    • betaX_United Kingdom_dim_1: 3
    • noise_chol_United Kingdom_corr_dim_0: 3
    • noise_chol_United Kingdom_corr_dim_1: 3
    • noise_chol_United Kingdom_stds_dim_0: 3
    • omega_United Kingdom_dim_0: 3
    • omega_United Kingdom_dim_1: 3
    • betaX_United States_dim_0: 46
    • betaX_United States_dim_1: 3
    • noise_chol_United States_corr_dim_0: 3
    • noise_chol_United States_corr_dim_1: 3
    • noise_chol_United States_stds_dim_0: 3
    • omega_United States_dim_0: 3
    • omega_United States_dim_1: 3
  • Coordinates: (73)
    • chain
      (chain)
      int64
      0 1 2 3

      array([0, 1, 2, 3])

    • draw
      (draw)
      int64
      0 1 2 3 4 ... 1996 1997 1998 1999

      array([   0,    1,    2, ..., 1997, 1998, 1999])

    • equations
      (equations)
      <U7
      'dl_gdp' 'dl_cons' 'dl_gfcf'

      array(['dl_gdp', 'dl_cons', 'dl_gfcf'], dtype='<U7')

    • lags
      (lags)
      int64
      1 2

      array([1, 2])

    • cross_vars
      (cross_vars)
      <U7
      'dl_gdp' 'dl_cons' 'dl_gfcf'

      array(['dl_gdp', 'dl_cons', 'dl_gfcf'], dtype='<U7')

    • omega_global_dim_0
      (omega_global_dim_0)
      int64
      0 1 2 3 4 5

      array([0, 1, 2, 3, 4, 5])

    • noise_chol_Australia_dim_0
      (noise_chol_Australia_dim_0)
      int64
      0 1 2 3 4 5

      array([0, 1, 2, 3, 4, 5])

    • noise_chol_Canada_dim_0
      (noise_chol_Canada_dim_0)
      int64
      0 1 2 3 4 5

      array([0, 1, 2, 3, 4, 5])

    • noise_chol_Chile_dim_0
      (noise_chol_Chile_dim_0)
      int64
      0 1 2 3 4 5

      array([0, 1, 2, 3, 4, 5])

    • noise_chol_Ireland_dim_0
      (noise_chol_Ireland_dim_0)
      int64
      0 1 2 3 4 5

      array([0, 1, 2, 3, 4, 5])

    • noise_chol_New Zealand_dim_0
      (noise_chol_New Zealand_dim_0)
      int64
      0 1 2 3 4 5

      array([0, 1, 2, 3, 4, 5])

    • noise_chol_South Africa_dim_0
      (noise_chol_South Africa_dim_0)
      int64
      0 1 2 3 4 5

      array([0, 1, 2, 3, 4, 5])

    • noise_chol_United Kingdom_dim_0
      (noise_chol_United Kingdom_dim_0)
      int64
      0 1 2 3 4 5

      array([0, 1, 2, 3, 4, 5])

    • noise_chol_United States_dim_0
      (noise_chol_United States_dim_0)
      int64
      0 1 2 3 4 5

      array([0, 1, 2, 3, 4, 5])

    • omega_global_corr_dim_0
      (omega_global_corr_dim_0)
      int64
      0 1 2

      array([0, 1, 2])

    • omega_global_corr_dim_1
      (omega_global_corr_dim_1)
      int64
      0 1 2

      array([0, 1, 2])

    • omega_global_stds_dim_0
      (omega_global_stds_dim_0)
      int64
      0 1 2

      array([0, 1, 2])

    • betaX_Australia_dim_0
      (betaX_Australia_dim_0)
      int64
      0 1 2 3 4 5 6 ... 43 44 45 46 47 48

      array([ 0,  1,  2,  3,  4,  5,  6,  7,  8,  9, 10, 11, 12, 13, 14, 15, 16, 17,
             18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35,
             36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48])

    • betaX_Australia_dim_1
      (betaX_Australia_dim_1)
      int64
      0 1 2

      array([0, 1, 2])

    • noise_chol_Australia_corr_dim_0
      (noise_chol_Australia_corr_dim_0)
      int64
      0 1 2

      array([0, 1, 2])

    • noise_chol_Australia_corr_dim_1
      (noise_chol_Australia_corr_dim_1)
      int64
      0 1 2

      array([0, 1, 2])

    • noise_chol_Australia_stds_dim_0
      (noise_chol_Australia_stds_dim_0)
      int64
      0 1 2

      array([0, 1, 2])

    • omega_Australia_dim_0
      (omega_Australia_dim_0)
      int64
      0 1 2

      array([0, 1, 2])

    • omega_Australia_dim_1
      (omega_Australia_dim_1)
      int64
      0 1 2

      array([0, 1, 2])

    • betaX_Canada_dim_0
      (betaX_Canada_dim_0)
      int64
      0 1 2 3 4 5 6 ... 16 17 18 19 20 21

      array([ 0,  1,  2,  3,  4,  5,  6,  7,  8,  9, 10, 11, 12, 13, 14, 15, 16, 17,
             18, 19, 20, 21])

    • betaX_Canada_dim_1
      (betaX_Canada_dim_1)
      int64
      0 1 2

      array([0, 1, 2])

    • noise_chol_Canada_corr_dim_0
      (noise_chol_Canada_corr_dim_0)
      int64
      0 1 2

      array([0, 1, 2])

    • noise_chol_Canada_corr_dim_1
      (noise_chol_Canada_corr_dim_1)
      int64
      0 1 2

      array([0, 1, 2])

    • noise_chol_Canada_stds_dim_0
      (noise_chol_Canada_stds_dim_0)
      int64
      0 1 2

      array([0, 1, 2])

    • omega_Canada_dim_0
      (omega_Canada_dim_0)
      int64
      0 1 2

      array([0, 1, 2])

    • omega_Canada_dim_1
      (omega_Canada_dim_1)
      int64
      0 1 2

      array([0, 1, 2])

    • betaX_Chile_dim_0
      (betaX_Chile_dim_0)
      int64
      0 1 2 3 4 5 6 ... 43 44 45 46 47 48

      array([ 0,  1,  2,  3,  4,  5,  6,  7,  8,  9, 10, 11, 12, 13, 14, 15, 16, 17,
             18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35,
             36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48])

    • betaX_Chile_dim_1
      (betaX_Chile_dim_1)
      int64
      0 1 2

      array([0, 1, 2])

    • noise_chol_Chile_corr_dim_0
      (noise_chol_Chile_corr_dim_0)
      int64
      0 1 2

      array([0, 1, 2])

    • noise_chol_Chile_corr_dim_1
      (noise_chol_Chile_corr_dim_1)
      int64
      0 1 2

      array([0, 1, 2])

    • noise_chol_Chile_stds_dim_0
      (noise_chol_Chile_stds_dim_0)
      int64
      0 1 2

      array([0, 1, 2])

    • omega_Chile_dim_0
      (omega_Chile_dim_0)
      int64
      0 1 2

      array([0, 1, 2])

    • omega_Chile_dim_1
      (omega_Chile_dim_1)
      int64
      0 1 2

      array([0, 1, 2])

    • betaX_Ireland_dim_0
      (betaX_Ireland_dim_0)
      int64
      0 1 2 3 4 5 6 ... 43 44 45 46 47 48

      array([ 0,  1,  2,  3,  4,  5,  6,  7,  8,  9, 10, 11, 12, 13, 14, 15, 16, 17,
             18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35,
             36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48])

    • betaX_Ireland_dim_1
      (betaX_Ireland_dim_1)
      int64
      0 1 2

      array([0, 1, 2])

    • noise_chol_Ireland_corr_dim_0
      (noise_chol_Ireland_corr_dim_0)
      int64
      0 1 2

      array([0, 1, 2])

    • noise_chol_Ireland_corr_dim_1
      (noise_chol_Ireland_corr_dim_1)
      int64
      0 1 2

      array([0, 1, 2])

    • noise_chol_Ireland_stds_dim_0
      (noise_chol_Ireland_stds_dim_0)
      int64
      0 1 2

      array([0, 1, 2])

    • omega_Ireland_dim_0
      (omega_Ireland_dim_0)
      int64
      0 1 2

      array([0, 1, 2])

    • omega_Ireland_dim_1
      (omega_Ireland_dim_1)
      int64
      0 1 2

      array([0, 1, 2])

    • betaX_New Zealand_dim_0
      (betaX_New Zealand_dim_0)
      int64
      0 1 2 3 4 5 6 ... 35 36 37 38 39 40

      array([ 0,  1,  2,  3,  4,  5,  6,  7,  8,  9, 10, 11, 12, 13, 14, 15, 16, 17,
             18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35,
             36, 37, 38, 39, 40])

    • betaX_New Zealand_dim_1
      (betaX_New Zealand_dim_1)
      int64
      0 1 2

      array([0, 1, 2])

    • noise_chol_New Zealand_corr_dim_0
      (noise_chol_New Zealand_corr_dim_0)
      int64
      0 1 2

      array([0, 1, 2])

    • noise_chol_New Zealand_corr_dim_1
      (noise_chol_New Zealand_corr_dim_1)
      int64
      0 1 2

      array([0, 1, 2])

    • noise_chol_New Zealand_stds_dim_0
      (noise_chol_New Zealand_stds_dim_0)
      int64
      0 1 2

      array([0, 1, 2])

    • omega_New Zealand_dim_0
      (omega_New Zealand_dim_0)
      int64
      0 1 2

      array([0, 1, 2])

    • omega_New Zealand_dim_1
      (omega_New Zealand_dim_1)
      int64
      0 1 2

      array([0, 1, 2])

    • betaX_South Africa_dim_0
      (betaX_South Africa_dim_0)
      int64
      0 1 2 3 4 5 6 ... 43 44 45 46 47 48

      array([ 0,  1,  2,  3,  4,  5,  6,  7,  8,  9, 10, 11, 12, 13, 14, 15, 16, 17,
             18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35,
             36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48])

    • betaX_South Africa_dim_1
      (betaX_South Africa_dim_1)
      int64
      0 1 2

      array([0, 1, 2])

    • noise_chol_South Africa_corr_dim_0
      (noise_chol_South Africa_corr_dim_0)
      int64
      0 1 2

      array([0, 1, 2])

    • noise_chol_South Africa_corr_dim_1
      (noise_chol_South Africa_corr_dim_1)
      int64
      0 1 2

      array([0, 1, 2])

    • noise_chol_South Africa_stds_dim_0
      (noise_chol_South Africa_stds_dim_0)
      int64
      0 1 2

      array([0, 1, 2])

    • omega_South Africa_dim_0
      (omega_South Africa_dim_0)
      int64
      0 1 2

      array([0, 1, 2])

    • omega_South Africa_dim_1
      (omega_South Africa_dim_1)
      int64
      0 1 2

      array([0, 1, 2])

    • betaX_United Kingdom_dim_0
      (betaX_United Kingdom_dim_0)
      int64
      0 1 2 3 4 5 6 ... 43 44 45 46 47 48

      array([ 0,  1,  2,  3,  4,  5,  6,  7,  8,  9, 10, 11, 12, 13, 14, 15, 16, 17,
             18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35,
             36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48])

    • betaX_United Kingdom_dim_1
      (betaX_United Kingdom_dim_1)
      int64
      0 1 2

      array([0, 1, 2])

    • noise_chol_United Kingdom_corr_dim_0
      (noise_chol_United Kingdom_corr_dim_0)
      int64
      0 1 2

      array([0, 1, 2])

    • noise_chol_United Kingdom_corr_dim_1
      (noise_chol_United Kingdom_corr_dim_1)
      int64
      0 1 2

      array([0, 1, 2])

    • noise_chol_United Kingdom_stds_dim_0
      (noise_chol_United Kingdom_stds_dim_0)
      int64
      0 1 2

      array([0, 1, 2])

    • omega_United Kingdom_dim_0
      (omega_United Kingdom_dim_0)
      int64
      0 1 2

      array([0, 1, 2])

    • omega_United Kingdom_dim_1
      (omega_United Kingdom_dim_1)
      int64
      0 1 2

      array([0, 1, 2])

    • betaX_United States_dim_0
      (betaX_United States_dim_0)
      int64
      0 1 2 3 4 5 6 ... 40 41 42 43 44 45

      array([ 0,  1,  2,  3,  4,  5,  6,  7,  8,  9, 10, 11, 12, 13, 14, 15, 16, 17,
             18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35,
             36, 37, 38, 39, 40, 41, 42, 43, 44, 45])

    • betaX_United States_dim_1
      (betaX_United States_dim_1)
      int64
      0 1 2

      array([0, 1, 2])

    • noise_chol_United States_corr_dim_0
      (noise_chol_United States_corr_dim_0)
      int64
      0 1 2

      array([0, 1, 2])

    • noise_chol_United States_corr_dim_1
      (noise_chol_United States_corr_dim_1)
      int64
      0 1 2

      array([0, 1, 2])

    • noise_chol_United States_stds_dim_0
      (noise_chol_United States_stds_dim_0)
      int64
      0 1 2

      array([0, 1, 2])

    • omega_United States_dim_0
      (omega_United States_dim_0)
      int64
      0 1 2

      array([0, 1, 2])

    • omega_United States_dim_1
      (omega_United States_dim_1)
      int64
      0 1 2

      array([0, 1, 2])

  • Data variables: (80)
    • alpha_hat_location
      (chain, draw)
      float64
      0.01867 0.02452 ... 0.02525 0.02439

      array([[0.0186718 , 0.02451757, 0.02175917, ..., 0.02313991, 0.02264565,
              0.02262757],
             [0.02194229, 0.01975299, 0.01973764, ..., 0.02332028, 0.02396733,
              0.02430533],
             [0.02017885, 0.02004322, 0.01743769, ..., 0.02143034, 0.0220604 ,
              0.02622348],
             [0.01845575, 0.02208645, 0.01699277, ..., 0.02487232, 0.02524865,
              0.02439422]])

    • beta_hat_location
      (chain, draw)
      float64
      0.03707 0.03328 ... 0.01597 0.02013

      array([[0.03707199, 0.03328202, 0.03327573, ..., 0.02022314, 0.01849649,
              0.02157836],
             [0.02625807, 0.03075176, 0.03222849, ..., 0.02858588, 0.01833262,
              0.0215363 ],
             [0.03578886, 0.03454472, 0.03803878, ..., 0.02762439, 0.0293772 ,
              0.0225766 ],
             [0.02942673, 0.03678047, 0.03405673, ..., 0.02473977, 0.01597052,
              0.0201329 ]])

    • lag_coefs_Australia
      (chain, draw, equations, lags, cross_vars)
      float64
      0.03359 0.02897 ... -0.04637

      array([[[[[ 3.35876842e-02,  2.89656460e-02,  1.44346827e-02],
                [ 8.37580972e-02,  3.24134878e-02, -2.82482944e-02]],
      
               [[ 7.26090826e-02, -2.13751601e-02,  4.48405788e-02],
                [-8.62745446e-03,  6.50512197e-02,  3.53772829e-02]],
      
               [[ 1.33485138e-01, -1.01438292e-02, -3.84827532e-02],
                [ 8.71983706e-02,  4.94076769e-02,  1.65164026e-02]]],
      
      
              [[[-1.49945684e-02,  1.26595954e-01,  1.85231803e-02],
                [ 8.36634775e-02, -2.39762157e-02, -4.01462709e-02]],
      
               [[ 4.48792564e-03,  8.64514159e-02,  4.15399598e-02],
                [ 4.96201513e-02,  4.76304546e-02, -4.78025294e-03]],
      
               [[ 3.01187469e-02,  3.96725859e-03,  5.16570055e-02],
                [ 5.89717588e-02,  1.02783667e-01, -5.68183027e-02]]],
      
      
      ...
      
      
              [[[-6.09370080e-04, -4.28833919e-02, -1.72132262e-02],
                [ 8.35965353e-03,  4.55781405e-02, -2.42132324e-02]],
      
               [[ 4.88764274e-02,  6.16764673e-02,  1.71383871e-02],
                [ 3.83475664e-02,  6.11454731e-02,  1.19527231e-02]],
      
               [[-8.09687797e-02,  8.17902158e-03, -5.25417172e-03],
                [ 2.41407964e-02,  3.25160033e-03, -2.44207844e-02]]],
      
      
              [[[ 2.05738963e-02, -1.11911043e-02, -2.76806626e-02],
                [ 3.84035145e-02,  7.34061297e-02,  2.56814253e-02]],
      
               [[ 4.87554839e-02,  2.48335988e-02, -7.74723598e-03],
                [ 5.52062580e-02,  6.27619815e-02,  1.48180294e-03]],
      
               [[-8.57767638e-02, -5.80385978e-03,  3.99498228e-02],
                [ 1.82907424e-02,  5.53130978e-02, -4.63726851e-02]]]]])

    • alpha_Australia
      (chain, draw, equations)
      float64
      0.02263 0.02195 ... 0.0256 0.04313

      array([[[0.02263033, 0.0219483 , 0.02278174],
              [0.02092655, 0.02117198, 0.01957458],
              [0.02471809, 0.02338723, 0.02126247],
              ...,
              [0.02733054, 0.02529274, 0.02926754],
              [0.0229278 , 0.02485852, 0.02744026],
              [0.02545857, 0.024065  , 0.02478534]],
      
             [[0.02535366, 0.02349025, 0.0258179 ],
              [0.02633209, 0.02612907, 0.02978084],
              [0.02298526, 0.02043026, 0.02110987],
              ...,
              [0.02911641, 0.01716411, 0.02245609],
              [0.02612856, 0.02059014, 0.02068046],
              [0.0288257 , 0.02033768, 0.02226378]],
      
             [[0.02258029, 0.02479371, 0.03093723],
              [0.0258095 , 0.02523357, 0.02888035],
              [0.02555444, 0.02835614, 0.02272297],
              ...,
              [0.02168698, 0.02232613, 0.02013229],
              [0.02085286, 0.02223427, 0.02259567],
              [0.02968412, 0.02811583, 0.03453368]],
      
             [[0.02283776, 0.02056642, 0.020418  ],
              [0.02121562, 0.02447455, 0.01693719],
              [0.01891216, 0.01366135, 0.01818819],
              ...,
              [0.03010412, 0.02400799, 0.03880659],
              [0.03082631, 0.02208602, 0.0357919 ],
              [0.02795351, 0.02560223, 0.04313025]]])

    • lag_coefs_Canada
      (chain, draw, equations, lags, cross_vars)
      float64
      0.07658 0.1244 ... 0.05222

      array([[[[[ 7.65771654e-02,  1.24359779e-01,  4.76910322e-02],
                [ 2.93667122e-02,  3.72310073e-02,  3.49173993e-02]],
      
               [[ 4.41347272e-02,  8.81811011e-03, -3.05038254e-04],
                [ 4.78927391e-02, -4.02214926e-03,  8.59285906e-03]],
      
               [[ 5.10979503e-02,  6.56671799e-02, -6.60947485e-02],
                [-6.07279826e-03,  4.58702563e-03,  7.23134454e-02]]],
      
      
              [[[ 9.58053837e-03, -3.61069775e-02,  6.42945320e-02],
                [ 3.85629973e-02,  3.81227043e-02,  3.71742576e-02]],
      
               [[ 1.99385509e-02,  6.05511924e-02,  4.11373442e-02],
                [ 4.40550718e-02,  8.55328657e-02,  5.53053572e-02]],
      
               [[ 1.73913842e-02,  3.34697407e-02,  1.16211321e-01],
                [ 6.83408791e-02,  4.04932208e-02, -4.08216894e-03]]],
      
      
      ...
      
      
              [[[ 1.60683243e-02,  2.61087715e-02,  3.92718077e-02],
                [ 4.01146237e-03, -2.37060312e-02, -4.62161483e-02]],
      
               [[ 1.56423894e-02, -4.50955622e-02,  3.51574636e-02],
                [ 5.25022469e-02,  1.23002896e-01, -8.16030734e-03]],
      
               [[ 7.57467809e-02, -2.31002172e-02,  5.49980542e-03],
                [ 9.01656608e-02,  3.48274765e-02, -2.31388941e-02]]],
      
      
              [[[-3.26630109e-02,  8.19079238e-02,  4.89127987e-02],
                [ 4.26865954e-02,  7.20299244e-03,  4.26620550e-04]],
      
               [[-2.17148943e-02,  1.58301049e-02,  1.81258805e-02],
                [-9.93058176e-03,  6.71043977e-02, -2.33663183e-02]],
      
               [[ 4.33928770e-02,  8.33936906e-02, -3.14980137e-02],
                [ 2.91290443e-02, -4.29921752e-03,  5.22202592e-02]]]]])

    • alpha_Canada
      (chain, draw, equations)
      float64
      0.01466 0.0211 ... 0.02472 0.01323

      array([[[0.01465676, 0.02109877, 0.01855721],
              [0.02272014, 0.0171131 , 0.01590168],
              [0.01971124, 0.02032568, 0.02398538],
              ...,
              [0.02450623, 0.02726242, 0.02387   ],
              [0.01963401, 0.01932964, 0.02593143],
              [0.02264207, 0.02528133, 0.02215   ]],
      
             [[0.01932912, 0.01498189, 0.01999218],
              [0.01633058, 0.01809994, 0.01882801],
              [0.02273562, 0.02245996, 0.02561266],
              ...,
              [0.02284951, 0.02029153, 0.01529943],
              [0.02505905, 0.01790449, 0.015711  ],
              [0.02211575, 0.0200038 , 0.01910552]],
      
             [[0.02052051, 0.01468323, 0.01967417],
              [0.02064814, 0.02049906, 0.01690491],
              [0.0180907 , 0.01218556, 0.02297644],
              ...,
              [0.0162916 , 0.01964002, 0.02564671],
              [0.01835867, 0.01888253, 0.02585724],
              [0.02651413, 0.02532478, 0.02536538]],
      
             [[0.01227525, 0.00859114, 0.01227358],
              [0.01348817, 0.02417696, 0.0088522 ],
              [0.02154709, 0.01892863, 0.01997271],
              ...,
              [0.0095156 , 0.01107229, 0.01655292],
              [0.0125203 , 0.01218851, 0.01862845],
              [0.02285449, 0.02472482, 0.01322827]]])

    • lag_coefs_Chile
      (chain, draw, equations, lags, cross_vars)
      float64
      0.02434 0.07542 ... 0.0781 0.01202

      array([[[[[ 0.02433804,  0.07542013,  0.02079627],
                [ 0.02467259,  0.00924671,  0.03645728]],
      
               [[ 0.11158481, -0.00292094, -0.00202375],
                [ 0.04498318,  0.03563335,  0.05439888]],
      
               [[-0.01269364,  0.08447966,  0.1345423 ],
                [ 0.02703151,  0.10369712,  0.03123074]]],
      
      
              [[[ 0.0400249 ,  0.00464353, -0.00628709],
                [ 0.0246438 , -0.00507188,  0.07052514]],
      
               [[-0.00183431,  0.09928378,  0.03237165],
                [-0.01362285, -0.00625419,  0.11892922]],
      
               [[ 0.18241235, -0.03177573, -0.07682694],
                [-0.00521849,  0.05234479, -0.00809534]]],
      
      
      ...
      
      
              [[[-0.01113938,  0.0019725 ,  0.03888019],
                [-0.0062262 , -0.00483893,  0.04046326]],
      
               [[ 0.00299654,  0.01747632,  0.03686241],
                [ 0.02648647,  0.04897884,  0.06965917]],
      
               [[-0.0606741 ,  0.03266535,  0.03051538],
                [-0.00779615, -0.04198754,  0.02741326]]],
      
      
              [[[-0.05763529,  0.04684115,  0.05842114],
                [ 0.06032375, -0.01520761,  0.00817284]],
      
               [[ 0.05147328,  0.02202345,  0.03813707],
                [ 0.03425661, -0.04428136,  0.06632278]],
      
               [[-0.03186269,  0.02367396,  0.05876045],
                [ 0.04699741,  0.07809989,  0.01201971]]]]])

    • alpha_Chile
      (chain, draw, equations)
      float64
      0.01571 0.02137 ... 0.02319 0.01586

      array([[[0.0157132 , 0.02136831, 0.02045335],
              [0.02351699, 0.02662639, 0.03141462],
              [0.03286153, 0.02286942, 0.03075199],
              ...,
              [0.02658816, 0.03269706, 0.02478334],
              [0.02555073, 0.01428823, 0.02046823],
              [0.02267686, 0.03051695, 0.02624876]],
      
             [[0.03034501, 0.02961176, 0.03364585],
              [0.02170808, 0.02056791, 0.01763461],
              [0.03020966, 0.01999711, 0.02384438],
              ...,
              [0.02466762, 0.02259074, 0.02228189],
              [0.02398052, 0.02372222, 0.02535443],
              [0.02796878, 0.02258504, 0.03085559]],
      
             [[0.01955303, 0.02566435, 0.02335706],
              [0.02350364, 0.02081194, 0.02000074],
              [0.02316185, 0.02513018, 0.02467213],
              ...,
              [0.02045066, 0.02412166, 0.0248603 ],
              [0.02073028, 0.02140164, 0.02252704],
              [0.030537  , 0.03115226, 0.04309932]],
      
             [[0.01399888, 0.02231359, 0.01948238],
              [0.03077856, 0.01536788, 0.03785173],
              [0.02841149, 0.03715862, 0.04349375],
              ...,
              [0.02193738, 0.0220144 , 0.02608079],
              [0.02520517, 0.01965012, 0.02631976],
              [0.02767934, 0.02319005, 0.0158585 ]]])

    • lag_coefs_Ireland
      (chain, draw, equations, lags, cross_vars)
      float64
      -0.01475 0.0387 ... 0.08891 -0.0483

      array([[[[[-1.47458909e-02,  3.87000770e-02,  7.32095142e-02],
                [ 5.44968014e-02,  6.13786029e-02,  6.07706896e-02]],
      
               [[ 7.11516666e-02,  6.17419700e-02,  3.69797323e-02],
                [-2.28057433e-02,  2.31310597e-02,  7.40369221e-02]],
      
               [[ 4.21034377e-02,  8.53380497e-02,  2.10043775e-02],
                [ 6.44045030e-02,  2.85718044e-02,  4.66844083e-02]]],
      
      
              [[[-3.66079960e-02, -6.99503410e-02,  3.55270626e-02],
                [ 4.47186220e-02,  5.66331099e-02,  8.58598582e-02]],
      
               [[ 1.32912956e-01,  9.57010562e-02, -5.63016658e-02],
                [-2.51360288e-02,  5.79225409e-02,  6.21822960e-02]],
      
               [[ 4.97219669e-02,  1.14537321e-01,  1.07593179e-01],
                [ 7.35308871e-02,  2.34267153e-02,  2.96861721e-02]]],
      
      
      ...
      
      
              [[[-8.84380474e-02, -8.42599965e-02,  4.61872283e-02],
                [ 2.79902469e-02, -1.40869522e-02,  8.25633877e-02]],
      
               [[ 6.87530181e-02,  1.31929462e-01, -4.16510214e-02],
                [ 3.93040561e-02,  6.10045570e-02,  6.75494335e-02]],
      
               [[ 8.75675887e-02,  4.11261218e-02, -1.24124758e-02],
                [ 3.07071749e-02,  7.66659495e-02, -5.93595914e-02]]],
      
      
              [[[-1.74323530e-02, -3.22370525e-02,  4.50600308e-02],
                [-3.68440838e-02, -3.93261936e-02,  1.16347198e-01]],
      
               [[ 1.76288211e-01,  8.77909100e-02, -4.35165182e-02],
                [-8.67491049e-03,  7.67305270e-02,  1.00445039e-01]],
      
               [[-1.64839671e-02, -6.10096604e-02, -3.32595903e-03],
                [-1.71668080e-02,  8.89058437e-02, -4.82995669e-02]]]]])

    • alpha_Ireland
      (chain, draw, equations)
      float64
      0.02198 0.01418 ... 0.01683 0.02614

      array([[[ 0.02198322,  0.01418345,  0.02419023],
              [ 0.03777364,  0.01957305,  0.007676  ],
              [ 0.03905588,  0.00898405,  0.02174625],
              ...,
              [ 0.03748313,  0.00654185,  0.03192922],
              [ 0.04685017,  0.01413632,  0.01609315],
              [ 0.04041201,  0.00862381,  0.04599709]],
      
             [[ 0.03520116,  0.00864943,  0.00656473],
              [ 0.03829489,  0.00718548,  0.03974323],
              [ 0.02576244,  0.01144094,  0.0282918 ],
              ...,
              [ 0.0432292 ,  0.01897203,  0.02735446],
              [ 0.04027758,  0.015737  ,  0.02289279],
              [ 0.03741163,  0.01368131,  0.0235036 ]],
      
             [[ 0.03536222,  0.00628412,  0.02729948],
              [ 0.03195189,  0.00413109,  0.02516136],
              [ 0.03224617, -0.00497087,  0.01715696],
              ...,
              [ 0.0236229 ,  0.01416163,  0.0175816 ],
              [ 0.02379884,  0.01203721,  0.01973875],
              [ 0.03983179,  0.02813402,  0.01942888]],
      
             [[ 0.03169915,  0.01435424,  0.00716936],
              [ 0.02786021,  0.0175066 ,  0.02303785],
              [ 0.02952215,  0.0132017 ,  0.01848463],
              ...,
              [ 0.04300775,  0.01253962,  0.04658183],
              [ 0.0444028 ,  0.01022499,  0.04403121],
              [ 0.04460278,  0.01682959,  0.02614388]]])

    • lag_coefs_New Zealand
      (chain, draw, equations, lags, cross_vars)
      float64
      0.0048 0.05318 ... 0.04656 -0.0277

      array([[[[[ 4.79955216e-03,  5.31766056e-02,  2.48001324e-02],
                [ 5.58142948e-02,  1.47251580e-02,  1.04404015e-02]],
      
               [[ 3.81839725e-02,  7.30885639e-02,  1.76983648e-02],
                [ 5.93599488e-02,  1.11361964e-01,  4.43170275e-02]],
      
               [[ 6.40167465e-02,  1.36748394e-03,  1.17405811e-02],
                [ 5.95082083e-02,  7.40553746e-02,  3.81552533e-02]]],
      
      
              [[[ 8.78219915e-02, -6.00073761e-03,  4.07609942e-02],
                [ 2.35031517e-02,  7.66114780e-03, -1.93500127e-02]],
      
               [[ 2.80442830e-02,  6.12851857e-02,  3.56544049e-02],
                [ 5.68764616e-02,  2.83996406e-02,  2.45822496e-02]],
      
               [[ 3.56649231e-02,  5.96405911e-02,  8.16509026e-02],
                [ 2.51308596e-02,  1.76106189e-02,  1.55734961e-02]]],
      
      
      ...
      
      
              [[[ 6.08300123e-02,  5.40027130e-03,  2.18290830e-02],
                [-1.47997178e-02, -3.39122149e-02,  2.20944587e-03]],
      
               [[ 5.50643240e-02,  1.45434541e-02,  1.25605541e-02],
                [ 4.65713980e-02,  7.46702282e-02,  4.67125897e-02]],
      
               [[ 3.57338813e-02, -5.94263736e-03,  4.39900990e-02],
                [ 3.32299355e-02,  2.50841926e-03, -3.00312747e-02]]],
      
      
              [[[ 1.00552259e-02,  4.50610550e-02,  7.41251774e-03],
                [ 3.41258860e-02, -5.06182746e-02, -1.04310654e-02]],
      
               [[ 5.72570423e-02, -3.84271622e-02, -1.19819215e-02],
                [ 3.52150287e-02,  9.21245461e-02,  2.60604335e-02]],
      
               [[-2.53743801e-02, -1.13646205e-02,  1.13368406e-02],
                [-2.90074466e-02,  4.65603013e-02, -2.77021942e-02]]]]])

    • alpha_New Zealand
      (chain, draw, equations)
      float64
      0.01807 0.01578 ... 0.01983 0.03992

      array([[[0.01806595, 0.01578354, 0.02132896],
              [0.01849362, 0.01821667, 0.02721401],
              [0.02175469, 0.0210865 , 0.03053284],
              ...,
              [0.02166377, 0.02133174, 0.02287388],
              [0.02227288, 0.02121135, 0.04353785],
              [0.02431044, 0.02571715, 0.03797068]],
      
             [[0.01357315, 0.01525364, 0.03253792],
              [0.02149012, 0.01032409, 0.04364514],
              [0.01709379, 0.00976669, 0.01623808],
              ...,
              [0.01432591, 0.01743779, 0.018122  ],
              [0.01355899, 0.01595626, 0.0193063 ],
              [0.01456813, 0.02003352, 0.01938244]],
      
             [[0.01530257, 0.01052001, 0.01589447],
              [0.01779147, 0.01416527, 0.03140318],
              [0.01520138, 0.02154654, 0.01620615],
              ...,
              [0.02688245, 0.02381044, 0.02911095],
              [0.02494411, 0.02434003, 0.02838573],
              [0.01827265, 0.01760944, 0.02858284]],
      
             [[0.02083092, 0.01857572, 0.03654796],
              [0.0173904 , 0.01745286, 0.02767121],
              [0.01518223, 0.01778471, 0.01862866],
              ...,
              [0.02430962, 0.02117357, 0.027361  ],
              [0.02282666, 0.02391651, 0.03463807],
              [0.0229253 , 0.01982705, 0.03992305]]])

    • lag_coefs_South Africa
      (chain, draw, equations, lags, cross_vars)
      float64
      0.02541 0.0323 ... 0.03994 0.04386

      array([[[[[ 2.54095143e-02,  3.22996821e-02, -3.78097958e-02],
                [ 3.30784901e-02,  3.32517969e-02,  2.43080368e-02]],
      
               [[-9.86439293e-02,  4.45366969e-02, -6.30080609e-05],
                [ 8.70273005e-02,  5.25125138e-02,  4.04114465e-02]],
      
               [[ 9.69363170e-02,  2.63073323e-01,  6.80924159e-02],
                [ 3.98254154e-02, -5.09993065e-03,  1.62231177e-02]]],
      
      
              [[[ 9.36984734e-03, -2.09374358e-03,  6.01439063e-02],
                [-7.98620343e-03, -6.73846794e-03, -3.22391351e-02]],
      
               [[ 9.86833948e-02,  6.64104290e-02, -2.58380556e-02],
                [ 9.64834973e-02,  2.63595052e-02, -2.52072028e-03]],
      
               [[ 3.62143695e-02, -4.25291141e-02,  7.39053616e-02],
                [ 1.87797137e-02,  3.77284890e-02,  4.37549702e-03]]],
      
      
      ...
      
      
              [[[ 2.64687906e-02,  3.02834530e-02, -4.36897775e-02],
                [ 3.48406493e-02,  1.82883799e-02,  2.12566437e-02]],
      
               [[ 3.54839360e-03,  5.47190827e-02, -3.93874975e-02],
                [ 7.21056725e-02,  2.29115900e-02,  1.35507151e-02]],
      
               [[ 4.50271670e-02,  5.52450887e-02,  1.01087607e-01],
                [ 3.18211228e-02,  2.47540401e-02,  5.77444944e-03]]],
      
      
              [[[-2.76738599e-02,  8.16627740e-04, -4.45258332e-02],
                [ 7.58972502e-02,  1.59472376e-02,  1.02064434e-02]],
      
               [[ 4.77160550e-03,  1.77943203e-02, -3.34288369e-02],
                [ 1.34368769e-02,  1.81799799e-02,  6.96008594e-02]],
      
               [[ 1.21946612e-02,  1.53324684e-02,  3.92778531e-03],
                [-5.05276037e-02,  3.99390702e-02,  4.38554698e-02]]]]])

    • alpha_South Africa
      (chain, draw, equations)
      float64
      0.01901 0.02268 ... 0.02615 0.01921

      array([[[0.01901206, 0.02267808, 0.01252531],
              [0.02365439, 0.02239854, 0.01985251],
              [0.01989679, 0.0220024 , 0.02289861],
              ...,
              [0.02342958, 0.02782862, 0.0204841 ],
              [0.01941431, 0.02520382, 0.02561481],
              [0.01896969, 0.02357623, 0.00824644]],
      
             [[0.01886008, 0.01832178, 0.01410036],
              [0.02367257, 0.02362778, 0.01416356],
              [0.0225035 , 0.02658002, 0.00968991],
              ...,
              [0.02055409, 0.02657549, 0.02245432],
              [0.02386924, 0.02856589, 0.02115162],
              [0.02554601, 0.02735204, 0.01862188]],
      
             [[0.02579471, 0.02669597, 0.01457212],
              [0.02038627, 0.02124575, 0.01988502],
              [0.01889323, 0.02108477, 0.01104016],
              ...,
              [0.01864664, 0.02434247, 0.01947247],
              [0.01867105, 0.02427485, 0.01796539],
              [0.02647408, 0.02692301, 0.02550011]],
      
             [[0.02029671, 0.01952457, 0.01701635],
              [0.02484205, 0.0302312 , 0.01765515],
              [0.01887883, 0.01832262, 0.01998897],
              ...,
              [0.02211716, 0.0234445 , 0.01737949],
              [0.02049095, 0.02449048, 0.01372325],
              [0.01958324, 0.02615177, 0.0192084 ]]])

    • lag_coefs_United Kingdom
      (chain, draw, equations, lags, cross_vars)
      float64
      0.05761 0.0274 ... -0.001775

      array([[[[[ 0.05761089,  0.0274021 ,  0.06190151],
                [ 0.0303106 ,  0.02267695,  0.022874  ]],
      
               [[ 0.06043142,  0.03478302,  0.04597842],
                [ 0.07937197, -0.00305529,  0.03926115]],
      
               [[ 0.03332199,  0.0388056 ,  0.07837689],
                [ 0.06736559,  0.05133304,  0.01535437]]],
      
      
              [[[ 0.07256452,  0.03193285,  0.02712607],
                [-0.02385231, -0.00268805,  0.02936621]],
      
               [[ 0.02799926,  0.01307594,  0.00886335],
                [ 0.08689927,  0.05372776,  0.0417348 ]],
      
               [[ 0.02188457,  0.07145874,  0.00491692],
                [-0.01293862,  0.00302327,  0.08443964]]],
      
      
      ...
      
      
              [[[-0.03540654,  0.03918698, -0.0236554 ],
                [ 0.0313792 ,  0.00023517, -0.04371644]],
      
               [[-0.02134802,  0.01079886,  0.01746537],
                [-0.00471261,  0.01925858,  0.01601016]],
      
               [[ 0.01603853,  0.05085501,  0.0145626 ],
                [ 0.02313931,  0.01217526,  0.0396992 ]]],
      
      
              [[[-0.00831721,  0.03572049,  0.00071403],
                [ 0.05066002, -0.02539158, -0.04745072]],
      
               [[-0.02264026, -0.02155469,  0.0228943 ],
                [ 0.06722884,  0.06794606,  0.0012824 ]],
      
               [[ 0.04053666, -0.02507347,  0.00704099],
                [ 0.04290297,  0.03121881, -0.00177492]]]]])

    • alpha_United Kingdom
      (chain, draw, equations)
      float64
      0.01761 0.0174 ... 0.02397 0.03081

      array([[[0.01761044, 0.0173951 , 0.02129423],
              [0.0176642 , 0.01433993, 0.01677042],
              [0.02329868, 0.01875666, 0.02059026],
              ...,
              [0.01786654, 0.01739791, 0.01644063],
              [0.02238243, 0.02049453, 0.02055928],
              [0.02340852, 0.02267508, 0.02877013]],
      
             [[0.02386716, 0.02211543, 0.02609062],
              [0.02504201, 0.02045074, 0.02446627],
              [0.02175407, 0.01676955, 0.01927967],
              ...,
              [0.01627474, 0.01657221, 0.01809339],
              [0.01732528, 0.01775757, 0.02601687],
              [0.01766491, 0.0168034 , 0.02148137]],
      
             [[0.01928886, 0.0196265 , 0.02452796],
              [0.01989401, 0.01935756, 0.02009702],
              [0.01772464, 0.01579172, 0.01717696],
              ...,
              [0.02173498, 0.01841189, 0.01904664],
              [0.02109208, 0.01908113, 0.01839193],
              [0.02285666, 0.01746688, 0.0264231 ]],
      
             [[0.01553938, 0.01546997, 0.01883268],
              [0.02013144, 0.01803673, 0.02642818],
              [0.01576727, 0.0137904 , 0.01420119],
              ...,
              [0.02646206, 0.02333062, 0.03159167],
              [0.02633969, 0.0241074 , 0.03232729],
              [0.02580901, 0.02397482, 0.03080724]]])

    • lag_coefs_United States
      (chain, draw, equations, lags, cross_vars)
      float64
      0.05386 0.07003 ... 0.0723 0.004706

      array([[[[[ 0.05385766,  0.07003283, -0.01949482],
                [ 0.00329857,  0.09423554,  0.07803958]],
      
               [[ 0.06490934,  0.07647176,  0.05103275],
                [ 0.08451833, -0.0374088 ,  0.04119398]],
      
               [[ 0.05504028, -0.02860814,  0.13109432],
                [-0.00247949,  0.05276195,  0.06957375]]],
      
      
              [[[ 0.01604   ,  0.01100934, -0.03315874],
                [ 0.06344352,  0.01422943, -0.00157213]],
      
               [[ 0.00252157,  0.02109809, -0.03896577],
                [ 0.00764408,  0.09185135,  0.04494501]],
      
               [[ 0.03205271,  0.10364687,  0.0513285 ],
                [ 0.05215269,  0.00552455, -0.00398291]]],
      
      
      ...
      
      
              [[[-0.01745811,  0.00109955, -0.00234785],
                [ 0.03402061,  0.09196414,  0.02566072]],
      
               [[-0.02224305,  0.0419783 ,  0.04470546],
                [ 0.01403128, -0.02350721,  0.03120449]],
      
               [[ 0.02172906,  0.1183168 ,  0.08603979],
                [ 0.06071867,  0.06974237, -0.00941608]]],
      
      
              [[[ 0.04054993,  0.00168886,  0.00204798],
                [ 0.03383608,  0.10752412,  0.00560849]],
      
               [[-0.02446238,  0.04611171,  0.06851168],
                [-0.02977762,  0.05915644,  0.02482298]],
      
               [[ 0.02284061,  0.14261998,  0.06283344],
                [ 0.07870006,  0.0722998 ,  0.00470552]]]]])

    • alpha_United States
      (chain, draw, equations)
      float64
      0.01419 0.01439 ... 0.02238 0.01881

      array([[[0.01418759, 0.01438589, 0.01789529],
              [0.02598225, 0.02316987, 0.02425873],
              [0.02084087, 0.02086088, 0.02268168],
              ...,
              [0.0204412 , 0.0181257 , 0.02361468],
              [0.02663887, 0.02359841, 0.02279745],
              [0.02026212, 0.01972341, 0.02921508]],
      
             [[0.0175823 , 0.01768812, 0.02307349],
              [0.01971666, 0.02071566, 0.02032091],
              [0.02503186, 0.01945537, 0.03680978],
              ...,
              [0.02330623, 0.02334296, 0.02966311],
              [0.02803772, 0.02371988, 0.02919166],
              [0.02598188, 0.02355839, 0.0276434 ]],
      
             [[0.01639968, 0.02059404, 0.02225209],
              [0.01516595, 0.02000534, 0.02034232],
              [0.01458103, 0.01572419, 0.01855923],
              ...,
              [0.02262127, 0.02314291, 0.02062068],
              [0.02356728, 0.02304586, 0.01839952],
              [0.0255272 , 0.02383072, 0.02629042]],
      
             [[0.01706889, 0.01811566, 0.01869895],
              [0.02279406, 0.02093012, 0.02772462],
              [0.01559355, 0.01706438, 0.01418122],
              ...,
              [0.02425718, 0.02578526, 0.02210795],
              [0.02031301, 0.02141664, 0.02099948],
              [0.02015476, 0.02238341, 0.01881354]]])

    • rho
      (chain, draw)
      float64
      0.9738 0.9781 ... 0.9742 0.9753

      array([[0.97381057, 0.97811196, 0.97718909, ..., 0.97291982, 0.97309863,
              0.97185022],
             [0.97169609, 0.97574464, 0.98000959, ..., 0.97467665, 0.97241438,
              0.97316599],
             [0.9735359 , 0.97198473, 0.97272403, ..., 0.97850145, 0.97746482,
              0.96707703],
             [0.97773676, 0.98241421, 0.98392793, ..., 0.97368538, 0.97423528,
              0.97533662]])

    • alpha_hat_scale
      (chain, draw)
      float64
      0.03402 0.06921 ... 0.0618 0.05396

      array([[0.0340201 , 0.06921044, 0.04641818, ..., 0.05165564, 0.04568199,
              0.04795936],
             [0.04631599, 0.04024177, 0.05337683, ..., 0.05200098, 0.05838578,
              0.05937475],
             [0.03724151, 0.03813012, 0.04173683, ..., 0.02798101, 0.02871392,
              0.04856515],
             [0.04674297, 0.08268964, 0.03778358, ..., 0.06162338, 0.06179729,
              0.0539579 ]])

    • beta_hat_scale
      (chain, draw)
      float64
      0.1702 0.342 ... 0.1799 0.1808

      array([[0.17021182, 0.34198411, 0.26618006, ..., 0.06287413, 0.07082787,
              0.08768702],
             [0.3597106 , 0.27083859, 0.30066   , ..., 0.26574803, 0.25635952,
              0.22758884],
             [0.19117243, 0.15246495, 0.14473942, ..., 0.22679552, 0.21358656,
              0.18949933],
             [0.17265149, 0.19386224, 0.19044116, ..., 0.24260553, 0.17989111,
              0.18078723]])

    • omega_global
      (chain, draw, omega_global_dim_0)
      float64
      0.01219 0.01523 ... 0.02162

      array([[[ 0.01218822,  0.01522638,  0.00340886,  0.04335285,
               -0.00217308,  0.01861989],
              [ 0.01083866,  0.01506469,  0.00349949,  0.0472653 ,
               -0.00810183,  0.018163  ],
              [ 0.01259793,  0.01506935,  0.00208336,  0.04179166,
               -0.00406775,  0.01350414],
              ...,
              [ 0.01538368,  0.01404695,  0.00268523,  0.04535721,
               -0.00239042,  0.02258466],
              [ 0.01742328,  0.01408072,  0.00235776,  0.0409345 ,
               -0.00474418,  0.02801085],
              [ 0.01750076,  0.01519746,  0.00180543,  0.04712585,
               -0.00497156,  0.02631976]],
      
             [[ 0.0096274 ,  0.01478892,  0.00145199,  0.04426993,
               -0.00713694,  0.01616899],
              [ 0.00911955,  0.01458634,  0.00192268,  0.04352532,
               -0.00404308,  0.01334046],
              [ 0.01766926,  0.01318953,  0.00298321,  0.04399035,
               -0.00028403,  0.01900471],
      ...
              [ 0.01309073,  0.01593698,  0.00427304,  0.04297485,
               -0.00625585,  0.01492482],
              [ 0.0131297 ,  0.01589519,  0.00361034,  0.04235657,
               -0.00874078,  0.01485382],
              [ 0.00700433,  0.01694595,  0.00332786,  0.04951525,
               -0.00864561,  0.01417389]],
      
             [[ 0.01657584,  0.01618365,  0.00121653,  0.0422487 ,
               -0.00536544,  0.02459217],
              [ 0.01429305,  0.01678552,  0.00287854,  0.04766878,
               -0.00414733,  0.02612078],
              [ 0.01566869,  0.01544929,  0.00087778,  0.04375063,
               -0.00088749,  0.02315615],
              ...,
              [ 0.01586844,  0.01328996,  0.00212247,  0.04404664,
               -0.00792564,  0.01707153],
              [ 0.01742985,  0.01451352,  0.00181431,  0.04416283,
               -0.00880546,  0.01853252],
              [ 0.01696835,  0.01391377,  0.00294613,  0.04265286,
               -0.00773243,  0.02161597]]])

    • z_scale_beta_Australia
      (chain, draw)
      float64
      0.2373 0.1376 ... 0.1337 0.3954

      array([[0.23733251, 0.13758496, 0.19790107, ..., 0.2683509 , 0.43777321,
              0.35490719],
             [0.16970964, 0.21089276, 0.14752019, ..., 0.20887074, 0.23847507,
              0.22740404],
             [0.18774524, 0.14397091, 0.15803173, ..., 0.1643344 , 0.14389337,
              0.17155927],
             [0.10184759, 0.14977448, 0.3845752 , ..., 0.18333872, 0.13368225,
              0.39544404]])

    • z_scale_alpha_Australia
      (chain, draw)
      float64
      0.1813 0.08512 ... 0.1576 0.1759

      array([[0.18129685, 0.08512272, 0.0825424 , ..., 0.19052937, 0.15158669,
              0.06388572],
             [0.17619474, 0.153651  , 0.06209169, ..., 0.10879725, 0.08143188,
              0.06124614],
             [0.33806892, 0.49434597, 1.13783518, ..., 0.07934544, 0.07641461,
              0.12051502],
             [0.08740891, 0.18904214, 0.05906492, ..., 0.14159646, 0.15764165,
              0.17588977]])

    • noise_chol_Australia
      (chain, draw, noise_chol_Australia_dim_0)
      float64
      0.175 -0.242 ... 0.1645 0.5325

      array([[[ 1.75009064e-01, -2.41966458e-01,  3.77166882e-01,
                1.56158277e-01, -1.59097525e-01,  7.46226834e-01],
              [ 3.27286769e-01, -2.06759636e-01,  3.54521164e-01,
               -8.78404918e-02,  4.12028275e-01,  8.42911934e-01],
              [ 2.07376788e-01, -2.06733568e-01,  4.11655442e-01,
                2.57772407e-02,  1.69097846e-01,  9.34743848e-01],
              ...,
              [ 2.45074957e-02, -1.01309189e-01,  3.91599644e-01,
               -8.20973318e-04,  1.39181640e-02,  5.49412749e-01],
              [ 8.91305701e-02, -2.30866065e-01,  3.59675857e-01,
               -2.97897976e-03,  6.01460053e-02,  3.37379791e-01],
              [ 2.16267881e-02, -1.11576650e-01,  3.04429183e-01,
                1.22103651e-01, -5.15246121e-02,  4.76004283e-01]],
      
             [[ 1.80956346e-01, -3.70271679e-01,  3.33901352e-01,
                8.23575085e-02,  8.00168014e-02,  7.95469864e-01],
              [ 2.64017511e-01, -2.39610503e-01,  5.50213319e-01,
               -1.59290032e-01, -1.33132507e-01,  9.18250045e-01],
              [ 3.78297087e-02, -2.21234165e-01,  4.00785255e-01,
                8.51259660e-02,  1.06339001e-01,  7.79466870e-01],
      ...
              [ 2.79023071e-01, -1.51039405e-01,  3.01706251e-01,
                3.58180855e-01, -2.48669353e-01,  1.10849280e+00],
              [ 2.38854510e-01, -1.53208579e-01,  3.35600307e-01,
                3.42964310e-01, -2.13285861e-01,  1.03457056e+00],
              [ 2.83983860e-01, -1.71796239e-01,  2.64743634e-01,
               -1.51092936e-01,  2.46242864e-01,  7.41648021e-01]],
      
             [[ 3.88131454e-02, -2.57320192e-01,  4.46016074e-01,
                1.77476846e-01,  1.70444198e-01,  1.04851247e+00],
              [ 5.64098263e-02, -4.67351932e-01,  5.61366262e-01,
               -1.42738917e-01,  6.95320006e-02,  3.81719892e-01],
              [ 9.50186978e-02, -3.52880748e-01,  6.78903260e-01,
                1.26887043e-01,  1.46595764e-01,  1.12829866e+00],
              ...,
              [ 5.44019018e-02, -8.85788728e-02,  3.77625681e-01,
                1.10980108e-01, -3.72535830e-02,  5.80429028e-01],
              [ 1.19395831e-01, -1.42548367e-01,  4.40398013e-01,
                1.12601989e-01,  2.26750509e-02,  6.72758290e-01],
              [ 4.30490930e-02, -1.93142846e-01,  2.47198998e-01,
                1.32553510e-01,  1.64468953e-01,  5.32483910e-01]]])

    • z_scale_beta_Canada
      (chain, draw)
      float64
      0.2736 0.1216 ... 0.2629 0.1972

      array([[0.2735902 , 0.12162758, 0.11923719, ..., 0.13616515, 0.14870794,
              0.05126063],
             [0.14145914, 0.12747015, 0.0982708 , ..., 0.17180652, 0.11555273,
              0.16727532],
             [0.2060911 , 0.22955972, 0.26356065, ..., 0.08780278, 0.10534695,
              0.22093912],
             [0.32993518, 0.19789392, 0.39145888, ..., 0.21750251, 0.26293427,
              0.19716798]])

    • z_scale_alpha_Canada
      (chain, draw)
      float64
      0.08111 0.1227 ... 0.1777 0.2688

      array([[0.08110592, 0.12272377, 0.05527928, ..., 0.10023458, 0.07230248,
              0.12789033],
             [0.05879722, 0.06700424, 0.11058203, ..., 0.14818562, 0.16656002,
              0.14363989],
             [0.18159317, 0.25359104, 0.07573124, ..., 0.21241997, 0.19597401,
              0.04952498],
             [0.18317507, 0.17453329, 0.13894086, ..., 0.24241797, 0.1777248 ,
              0.26877818]])

    • noise_chol_Canada
      (chain, draw, noise_chol_Canada_dim_0)
      float64
      0.6638 0.0403 ... -0.02874 1.181

      array([[[ 6.63841785e-01,  4.02967263e-02,  2.04557467e-01,
               -3.10301667e-01,  1.25588803e-01,  1.01760068e+00],
              [ 6.72230622e-01, -4.74201546e-02,  3.33468200e-01,
               -3.04123311e-01, -4.22369969e-02,  8.59109258e-01],
              [ 4.57499126e-01, -5.57666085e-02,  3.18614921e-01,
               -1.03435905e-01,  8.60762345e-02,  6.93882000e-01],
              ...,
              [ 2.30208350e-01,  2.74176641e-02,  2.56026965e-01,
                2.01260051e-02, -6.28187911e-02,  4.99447487e-01],
              [ 5.83471852e-01,  2.55009302e-02,  2.77491150e-01,
               -7.29815653e-02,  5.98704180e-03,  5.32175073e-01],
              [ 1.87097085e-01, -4.50975162e-03,  2.83794397e-01,
               -2.83188386e-02, -5.74170966e-02,  1.14011854e-01]],
      
             [[ 6.89523056e-01, -2.17638947e-02,  3.82243288e-01,
               -6.11455949e-02, -1.92379821e-02,  8.70274743e-01],
              [ 5.55481211e-01, -5.85440097e-02,  4.65228228e-01,
               -1.53032878e-03, -1.32821915e-01,  7.89445881e-01],
              [ 4.53761398e-01,  1.59819847e-01,  4.83133151e-01,
               -3.05715714e-01, -1.73863908e-01,  7.85893772e-01],
      ...
              [ 4.85396113e-01, -3.85010996e-02,  2.33234358e-01,
               -5.22581485e-01,  4.28506714e-02,  1.00645794e+00],
              [ 3.46013361e-01, -1.84679330e-02,  1.96155466e-01,
               -5.02223862e-01,  6.40270519e-02,  1.10288891e+00],
              [ 8.72890641e-01,  4.78983043e-03,  2.11053539e-01,
                1.98180766e-01,  7.17155397e-02,  5.77998588e-01]],
      
             [[ 5.46223094e-01,  8.02505172e-02,  4.28484043e-01,
                4.69637940e-02,  9.00672883e-02,  2.69944183e-01],
              [ 6.57170687e-01, -6.57688587e-02,  4.63001795e-01,
               -2.95114470e-01, -3.89604532e-01,  1.08588097e+00],
              [ 2.75631216e-01, -1.73436251e-01,  5.19705110e-01,
               -2.65749997e-01, -2.14369730e-01,  9.95094373e-01],
              ...,
              [ 4.67895105e-01,  5.50273105e-02,  2.99271255e-01,
                9.60565736e-02, -3.34911241e-02,  7.01043032e-01],
              [ 6.05728593e-01,  3.43214520e-02,  2.83898860e-01,
                2.63613127e-01, -6.90725341e-02,  4.55452429e-01],
              [ 3.56213359e-01,  1.20525000e-01,  2.67727139e-01,
                2.76738914e-01, -2.87416099e-02,  1.18068692e+00]]])

    • z_scale_beta_Chile
      (chain, draw)
      float64
      0.229 0.1375 ... 0.1742 0.1706

      array([[0.22899545, 0.13745599, 0.26038696, ..., 0.13271286, 0.13996626,
              0.15617835],
             [0.26796844, 0.32397628, 0.24143166, ..., 0.25281944, 0.26285746,
              0.16012707],
             [0.20003227, 0.22413203, 0.30807896, ..., 0.14702232, 0.13655419,
              0.1611094 ],
             [0.12665211, 0.24503321, 0.18145351, ..., 0.16564633, 0.17421741,
              0.1706148 ]])

    • z_scale_alpha_Chile
      (chain, draw)
      float64
      0.07176 0.2501 ... 0.1016 0.1626

      array([[0.07175951, 0.25009334, 0.19247747, ..., 0.12144125, 0.14389656,
              0.1744608 ],
             [0.20995505, 0.06798136, 0.16792769, ..., 0.03781415, 0.07560244,
              0.09997186],
             [0.21493768, 0.29495032, 0.14100461, ..., 0.06206609, 0.07443024,
              0.14303804],
             [0.13749515, 0.22017398, 0.6602553 , ..., 0.11386145, 0.10160067,
              0.1626074 ]])

    • noise_chol_Chile
      (chain, draw, noise_chol_Chile_dim_0)
      float64
      1.271 0.9954 1.283 ... 0.5532 2.125

      array([[[ 1.2713373 ,  0.99536111,  1.28338935,  1.43952188,
               -0.69684319,  3.22514992],
              [ 1.40839471,  0.82535996,  1.42734938,  2.09533359,
                0.20054094,  2.56586225],
              [ 1.05662488,  0.98155735,  1.40916792,  2.25338675,
               -0.04921683,  2.57580404],
              ...,
              [ 1.02995934,  0.97970855,  1.26811632,  1.72261509,
               -0.43159677,  2.03247673],
              [ 0.76983079,  0.81360878,  1.21848554,  1.2396864 ,
               -0.11252982,  1.81461605],
              [ 0.99565962,  0.99407386,  1.25909894,  1.71498306,
               -0.62919271,  1.96900818]],
      
             [[ 0.91491713,  0.64726681,  1.17620428,  1.13147863,
               -0.547197  ,  1.88580175],
              [ 1.54426339,  1.47131482,  1.35847226,  1.30451326,
               -0.78581922,  2.46155797],
              [ 1.27900868,  1.54230622,  1.52963902,  1.83131565,
                0.5343465 ,  2.95908756],
      ...
              [ 1.24101022,  0.70036062,  1.73477873,  2.24664284,
               -0.29344026,  2.921228  ],
              [ 1.31056705,  0.69116523,  1.67466986,  2.01757443,
               -0.10579977,  2.69521769],
              [ 1.07192233,  0.70944004,  1.11569374,  1.23529904,
               -0.19623784,  2.13655411]],
      
             [[ 1.29850511,  1.28588941,  1.64259491,  1.7294742 ,
                0.0111462 ,  2.8531648 ],
              [ 1.52666923,  0.8594347 ,  1.75708998,  2.21872494,
               -0.79308502,  2.63176654],
              [ 1.5267606 ,  1.79104923,  2.16756641,  1.94223226,
                0.36577915,  3.31320725],
              ...,
              [ 0.87863276,  0.8645867 ,  1.48716868,  0.7839539 ,
                0.41107075,  2.68110651],
              [ 1.00752757,  0.84377287,  1.1272519 ,  0.996813  ,
                0.25069931,  2.33427424],
              [ 0.84373496,  1.00729207,  1.34513209,  1.64363374,
                0.55315572,  2.12510581]]])

    • z_scale_beta_Ireland
      (chain, draw)
      float64
      0.1352 0.1684 ... 0.3071 0.3112

      array([[0.13515041, 0.16841739, 0.30566275, ..., 1.48384029, 1.26618831,
              0.96436302],
             [0.3002465 , 0.28440437, 0.33272395, ..., 0.34859503, 0.79417514,
              0.92764539],
             [0.67713418, 0.6029362 , 0.81819988, ..., 0.09783051, 0.08830116,
              0.17834987],
             [0.51930341, 0.40452318, 0.60129802, ..., 0.24895538, 0.30705064,
              0.3112266 ]])

    • z_scale_alpha_Ireland
      (chain, draw)
      float64
      0.1537 0.2775 ... 0.3494 0.1915

      array([[0.15365594, 0.27748515, 0.18524841, ..., 0.23729754, 0.277995  ,
              0.45423572],
             [0.54173165, 0.39499058, 0.12902482, ..., 0.14727411, 0.19081259,
              0.22165099],
             [0.21476198, 0.35359638, 0.52720217, ..., 0.21613118, 0.23772488,
              0.18405737],
             [0.38242312, 0.17401459, 0.61464315, ..., 0.33708139, 0.34940602,
              0.19148278]])

    • noise_chol_Ireland
      (chain, draw, noise_chol_Ireland_dim_0)
      float64
      1.099 0.02963 ... 1.621 5.085

      array([[[ 1.09856315e+00,  2.96345808e-02,  8.88518456e-01,
                1.18432112e+00,  7.80034956e-01,  5.25735088e+00],
              [ 1.07918067e+00, -2.05821137e-01,  7.64516760e-01,
               -1.16674692e+00,  3.26435914e+00,  5.32583601e+00],
              [ 1.24444094e+00, -2.02728601e-01,  8.79825094e-01,
                1.53841085e-01,  2.59942547e+00,  6.25166488e+00],
              ...,
              [ 1.11717345e+00,  5.72925103e-03,  7.30154454e-01,
                1.10736309e+00,  9.78603280e-01,  4.12596194e+00],
              [ 7.93225416e-01,  3.96900413e-02,  7.30948192e-01,
                7.10023342e-01,  6.40733857e-01,  4.98412443e+00],
              [ 7.96916953e-01, -3.01712273e-01,  6.96183628e-01,
                5.40954711e-01,  2.35211699e-01,  4.32336375e+00]],
      
             [[ 1.20283767e+00, -1.12765130e-01,  5.36040832e-01,
               -1.27636978e-01, -1.13365143e-01,  4.65049433e+00],
              [ 1.53763364e+00, -1.42004911e-01,  7.42971220e-01,
                1.52130992e+00,  6.66403722e-01,  5.57555202e+00],
              [ 1.16328075e+00, -2.05732679e-02,  9.36285222e-01,
               -1.53102862e-01,  6.71542056e-01,  5.95187924e+00],
      ...
              [ 1.30702197e+00, -1.76249618e-02,  8.98338946e-01,
               -3.28047179e-01,  1.67962272e+00,  6.36003612e+00],
              [ 1.40896661e+00,  7.13161220e-02,  8.78038893e-01,
               -3.61588797e-01,  1.63284155e+00,  6.57950999e+00],
              [ 9.00442033e-01, -2.24069083e-01,  6.06522848e-01,
                8.79411998e-01,  5.61357327e-01,  4.00038854e+00]],
      
             [[ 1.18230319e+00,  4.55079986e-02,  1.19128657e+00,
               -4.81292673e-01,  2.06992190e+00,  5.61763730e+00],
              [ 1.60181970e+00, -3.19149032e-01,  1.24078737e+00,
                1.92005227e+00,  1.76821775e+00,  7.22578334e+00],
              [ 1.84183924e+00,  5.61535923e-02,  1.28691485e+00,
                8.02460978e-02,  1.53634315e+00,  7.22210371e+00],
              ...,
              [ 7.49490956e-01, -1.16600008e-01,  8.05857611e-01,
                5.68280518e-01,  1.15574604e+00,  4.22703637e+00],
              [ 9.77372681e-01, -3.38123856e-02,  8.61020572e-01,
                7.34992405e-01,  1.54307067e+00,  4.42657352e+00],
              [ 8.55023254e-01, -5.75545242e-02,  7.53220868e-01,
                4.80298630e-01,  1.62075372e+00,  5.08493460e+00]]])

    • z_scale_beta_New Zealand
      (chain, draw)
      float64
      0.1568 0.08317 ... 0.1449 0.2407

      array([[0.15683385, 0.08317042, 0.13644376, ..., 0.19817681, 0.17730541,
              0.22075204],
             [0.5867957 , 0.40664675, 0.35064204, ..., 0.05166904, 0.10526662,
              0.10598518],
             [0.13731709, 0.14729447, 0.12760717, ..., 0.31413699, 0.23158494,
              0.20586101],
             [0.21346263, 0.10403213, 0.0915345 , ..., 0.11785439, 0.14485999,
              0.24066193]])

    • z_scale_alpha_New Zealand
      (chain, draw)
      float64
      0.06729 0.1558 ... 0.0909 0.1513

      array([[0.06728825, 0.15575064, 0.08057372, ..., 0.07220709, 0.45988372,
              0.23094846],
             [0.16929306, 0.32510334, 0.21386455, ..., 0.11509867, 0.17749332,
              0.22863279],
             [0.18692619, 0.23632348, 0.161856  , ..., 0.15370496, 0.1313317 ,
              0.14631651],
             [0.2057581 , 0.12671456, 0.08567276, ..., 0.1089957 , 0.09089895,
              0.15134683]])

    • noise_chol_New Zealand
      (chain, draw, noise_chol_New Zealand_dim_0)
      float64
      0.3045 -0.06226 ... 0.2427 0.9673

      array([[[ 3.04534370e-01, -6.22634500e-02,  2.30251224e-01,
                2.01567722e-01,  2.65176062e-01,  1.06972539e+00],
              [ 3.82169968e-01, -4.06752918e-02,  4.63471842e-01,
                1.48383846e-01, -2.94155889e-01,  1.25174283e+00],
              [ 2.55826468e-01, -1.03929812e-01,  3.52208684e-01,
                1.45533050e-03, -3.15286904e-01,  1.34032233e+00],
              ...,
              [ 2.05796473e-01, -5.65038526e-02,  2.72676759e-01,
                5.95319409e-02, -3.31483910e-03,  1.01420246e+00],
              [ 4.82275138e-02,  6.49698870e-03,  3.52252939e-01,
                3.08376854e-01, -7.09945453e-02,  8.00374888e-01],
              [ 9.96422216e-02, -5.69869594e-02,  3.13139052e-01,
                1.36687914e-02,  3.74159443e-01,  6.01404006e-01]],
      
             [[ 2.96598158e-01, -1.08394671e-01,  2.60064930e-01,
                1.00045077e-01,  3.19963468e-01,  1.19235821e+00],
              [ 3.68460688e-01, -3.49347948e-02,  2.83659682e-01,
                3.45677041e-01,  5.39216581e-01,  1.45119058e+00],
              [ 2.66135207e-02,  9.64662349e-03,  3.33401467e-01,
                2.63245444e-01,  6.99199673e-02,  1.46319812e+00],
      ...
              [ 3.26785762e-01, -4.75896942e-03,  3.03815676e-01,
                3.38326213e-01,  2.46681368e-01,  1.25811353e+00],
              [ 2.97884495e-01,  1.45474559e-02,  3.52891674e-01,
                3.54507591e-01,  2.40356352e-01,  1.30447621e+00],
              [ 3.22936817e-01, -7.71868518e-02,  3.44787980e-01,
                3.25989775e-01,  1.82560741e-01,  9.62272141e-01]],
      
             [[ 1.13775785e-01, -1.82756720e-01,  4.41427531e-01,
                5.97232948e-03, -2.33164515e-01,  9.26564865e-01],
              [ 1.42230904e-01, -1.63438802e-01,  4.09825107e-01,
                2.92795734e-01,  4.23615387e-01,  8.43114622e-01],
              [ 7.12239451e-02, -2.82156301e-01,  5.83461936e-01,
                8.92206268e-03, -1.95493032e-01,  1.13518904e+00],
              ...,
              [ 3.32437466e-03, -1.37439148e-01,  3.00861920e-01,
                4.94537599e-01,  3.04668942e-01,  1.37290872e+00],
              [ 3.17245931e-03, -7.99550666e-02,  3.00059226e-01,
                3.14103380e-01,  2.40498251e-01,  1.06737550e+00],
              [ 1.14414877e-03, -7.99456081e-02,  3.98605313e-01,
                3.91641437e-01,  2.42681961e-01,  9.67280276e-01]]])

    • z_scale_beta_South Africa
      (chain, draw)
      float64
      0.3028 0.1277 ... 0.1921 0.182

      array([[0.30279332, 0.12767831, 0.15688923, ..., 0.11106397, 0.07656958,
              0.15029139],
             [0.16064704, 0.23639388, 0.25754659, ..., 0.21746958, 0.10513224,
              0.18164775],
             [0.195663  , 0.35295286, 0.22305478, ..., 0.19855045, 0.19005038,
              0.24907922],
             [0.36338798, 0.18413234, 0.33847675, ..., 0.14802796, 0.19205473,
              0.18199475]])

    • z_scale_alpha_South Africa
      (chain, draw)
      float64
      0.1202 0.1349 ... 0.09006 0.285

      array([[0.12015358, 0.13493375, 0.0648358 , ..., 0.0919638 , 0.11024545,
              0.15766595],
             [0.19301864, 0.10122474, 0.17276421, ..., 0.15145001, 0.09511091,
              0.10969005],
             [0.19955557, 0.10092923, 0.10426572, ..., 0.22171558, 0.24340049,
              0.05818205],
             [0.09480666, 0.17856244, 0.08669728, ..., 0.10470687, 0.09005743,
              0.28504025]])

    • noise_chol_South Africa
      (chain, draw, noise_chol_South Africa_dim_0)
      float64
      0.5349 0.1351 ... 0.2843 1.149

      array([[[ 0.53491119,  0.13506689,  0.40925099,  0.43060671,
               -0.04671164,  1.0742078 ],
              [ 0.45006859,  0.07702614,  0.34843147, -0.02380481,
                0.80738061,  1.36785175],
              [ 0.52911664,  0.13904279,  0.41561976,  0.00761154,
                0.44446315,  1.71151233],
              ...,
              [ 0.23929478,  0.09108124,  0.29150512,  0.10614043,
                0.4239166 ,  1.44119576],
              [ 0.14620517,  0.21860656,  0.39451119,  0.09698263,
                0.15418555,  0.74159188],
              [ 0.28107478,  0.06335196,  0.34141938,  0.14266915,
                0.30526329,  1.100891  ]],
      
             [[ 0.49119883,  0.15763616,  0.31821425,  0.13000937,
                0.3455772 ,  1.17951536],
              [ 0.49160659,  0.07070707,  0.36609474,  0.07224417,
                0.22384536,  0.92835412],
              [ 0.25065236,  0.13493957,  0.48287582, -0.01236825,
                0.54147728,  1.49648292],
      ...
              [ 0.40043675,  0.12059527,  0.36182001,  0.10638281,
                0.6239572 ,  1.4541244 ],
              [ 0.43754413,  0.11387724,  0.36797442,  0.15256836,
                0.55618488,  1.36590003],
              [ 0.50844278,  0.09389214,  0.28417363,  0.05590844,
                0.04556554,  1.03091337]],
      
             [[ 0.26213754,  0.04139005,  0.42227785,  0.04647854,
                0.3332211 ,  1.07929115],
              [ 0.51324612,  0.19302037,  0.48696068,  0.15771725,
                0.1630655 ,  1.01446079],
              [ 0.26241434, -0.06503686,  0.65109777, -0.15114364,
                0.40048984,  1.62352346],
              ...,
              [ 0.30151799,  0.30066605,  0.53213137,  0.15784736,
                0.24558049,  0.96060019],
              [ 0.29867705,  0.2828084 ,  0.63986031,  0.14439767,
                0.23703673,  0.82412247],
              [ 0.38222619,  0.30634978,  0.30199813,  0.27346263,
                0.28426877,  1.14890924]]])

    • z_scale_beta_United Kingdom
      (chain, draw)
      float64
      0.1376 0.09737 ... 0.1359 0.1997

      array([[0.13760451, 0.09736721, 0.12133271, ..., 0.38925306, 0.31667518,
              0.22890316],
             [0.08038653, 0.12553462, 0.11477293, ..., 0.10769304, 0.10138577,
              0.09951663],
             [0.18279412, 0.15005027, 0.20712825, ..., 0.27319416, 0.28391667,
              0.2400759 ],
             [0.29275696, 0.32307963, 0.20115288, ..., 0.1389538 , 0.13585209,
              0.19965343]])

    • z_scale_alpha_United Kingdom
      (chain, draw)
      float64
      0.1097 0.09583 ... 0.1165 0.1876

      array([[0.10966504, 0.09583278, 0.13833385, ..., 0.09903016, 0.27157237,
              0.07406357],
             [0.28040022, 0.29537069, 0.16468849, ..., 0.20401608, 0.14859831,
              0.18059844],
             [0.1275927 , 0.12371497, 0.10679124, ..., 0.11174293, 0.09064222,
              0.11041517],
             [0.16563187, 0.07109435, 0.21548179, ..., 0.08576826, 0.11648584,
              0.18761744]])

    • noise_chol_United Kingdom
      (chain, draw, noise_chol_United Kingdom_dim_0)
      float64
      0.5181 0.1999 ... -0.1428 0.2923

      array([[[ 0.51805797,  0.19992544,  0.30611624, -0.03454922,
               -0.01727734,  0.41038445],
              [ 0.68063806,  0.17285   ,  0.27621605, -0.13650163,
                0.02689844,  0.63340957],
              [ 0.51016555,  0.07968407,  0.35528676, -0.18907501,
                0.04373098,  0.57833823],
              ...,
              [ 0.49340154,  0.22100705,  0.28635307, -0.06541354,
                0.02756904,  0.41131211],
              [ 0.27505083,  0.1507085 ,  0.31188928, -0.02256363,
               -0.01017282,  0.1454976 ],
              [ 0.50307347,  0.21146626,  0.35233846, -0.00891876,
               -0.01109241,  0.08418704]],
      
             [[ 0.6697906 ,  0.28757484,  0.29081772,  0.06310447,
                0.05003137,  0.7282122 ],
              [ 0.63231443,  0.20961938,  0.35221502,  0.08923737,
               -0.0575837 ,  0.8520046 ],
              [ 0.33083785,  0.09791569,  0.43926716, -0.2223944 ,
               -0.02075778,  0.89974798],
      ...
              [ 0.63094498,  0.20722517,  0.26024145, -0.03947783,
                0.06077336,  0.61679501],
              [ 0.65253291,  0.23846856,  0.26753542, -0.02718829,
                0.08001931,  0.68236906],
              [ 0.55743991,  0.11498019,  0.19110445, -0.17102278,
               -0.12158564,  0.48314845]],
      
             [[ 0.45621561,  0.21430995,  0.43111356, -0.02009445,
               -0.0292364 ,  0.14654888],
              [ 0.75799236,  0.23109576,  0.45407524, -0.11053904,
                0.00506073,  0.41793986],
              [ 0.73309182,  0.20437958,  0.70501178, -0.0333804 ,
               -0.02803683,  0.2328034 ],
              ...,
              [ 0.35197736,  0.19878206,  0.34689516, -0.07355243,
                0.14105923,  0.66148832],
              [ 0.33940493,  0.14350584,  0.35364014, -0.06468686,
                0.08147527,  0.49926483],
              [ 0.49475088,  0.34038341,  0.36892313, -0.03643964,
               -0.14280008,  0.2922645 ]]])

    • z_scale_beta_United States
      (chain, draw)
      float64
      0.1896 0.1494 ... 0.2437 0.2543

      array([[0.18958107, 0.1494162 , 0.13635679, ..., 0.15827189, 0.15912714,
              0.13280968],
             [0.12184466, 0.21663823, 0.22549997, ..., 0.09356525, 0.10630629,
              0.08359141],
             [0.41350269, 0.50259608, 0.45436826, ..., 0.1459533 , 0.14197894,
              0.18436221],
             [0.10960259, 0.06220923, 0.08655352, ..., 0.21524427, 0.24374299,
              0.25433995]])

    • z_scale_alpha_United States
      (chain, draw)
      float64
      0.2781 0.05996 ... 0.07085 0.1986

      array([[0.27805843, 0.05995524, 0.09545307, ..., 0.08129427, 0.13309833,
              0.11127608],
             [0.0663578 , 0.04932191, 0.21701084, ..., 0.077368  , 0.05992179,
              0.07399188],
             [0.10565687, 0.08574053, 0.07569111, ..., 0.11796192, 0.10216897,
              0.14909703],
             [0.08916109, 0.09249728, 0.141727  , ..., 0.10454905, 0.07085149,
              0.19861092]])

    • noise_chol_United States
      (chain, draw, noise_chol_United States_dim_0)
      float64
      0.3961 -0.02142 ... 0.03923

      array([[[ 3.96101210e-01, -2.14229339e-02,  1.71805163e-01,
                2.88551200e-02, -3.00898234e-02,  1.24734102e-01],
              [ 5.03002570e-01, -1.43405244e-02,  1.63154102e-01,
                5.04905115e-02, -2.63637879e-02,  3.02538415e-01],
              [ 4.04993670e-01,  3.04129759e-02,  2.90241912e-01,
                5.31442601e-02, -1.89588203e-02,  1.61462826e-01],
              ...,
              [ 2.53086948e-01, -5.78746877e-02,  2.17718052e-01,
               -1.25685048e-02, -1.17879993e-02,  4.68672641e-02],
              [ 1.83608671e-01,  2.04228355e-02,  1.46513849e-01,
                1.16691629e-02,  2.42975744e-03,  1.02663465e-01],
              [ 1.37632782e-01, -1.61296916e-02,  2.69887933e-01,
                5.19367162e-02,  2.34998753e-02,  2.43429048e-01]],
      
             [[ 3.39014250e-01, -1.43225055e-01,  2.47521763e-01,
               -8.63219548e-02,  1.72502016e-02,  1.20696676e-01],
              [ 4.61999281e-01, -1.06880397e-01,  2.19037221e-01,
               -1.53294265e-01, -1.68548360e-01,  3.12962460e-01],
              [ 1.82627588e-01, -2.72004972e-02,  2.06479878e-01,
                3.62971802e-02,  4.38487019e-02,  1.41787948e-01],
      ...
              [ 4.75538859e-01,  1.25698626e-03,  1.60342209e-01,
                2.38086815e-01,  1.16724900e-01,  4.99531795e-01],
              [ 4.79690965e-01, -6.31750907e-03,  1.52214873e-01,
                2.48485977e-01,  1.27297589e-01,  3.53743305e-01],
              [ 5.48080699e-01, -2.28229355e-03,  1.23535355e-01,
               -1.00901044e-02,  2.00580588e-02,  1.92498698e-01]],
      
             [[ 3.58773908e-01, -6.12252628e-02,  2.41452951e-01,
                1.47961304e-02, -1.48080351e-02,  7.77483716e-02],
              [ 5.36307260e-01, -7.16324745e-02,  2.83227906e-01,
               -4.25654389e-03,  1.64294962e-02,  8.98516510e-02],
              [ 4.56463393e-01, -4.11304643e-02,  4.90980148e-01,
                9.77820024e-03, -1.82103534e-02,  1.15329317e-01],
              ...,
              [ 2.48958959e-01,  2.75594740e-02,  3.03903081e-01,
                1.03640678e-03,  4.39198702e-03,  5.59877989e-02],
              [ 1.78786256e-01, -1.96203168e-02,  2.30191909e-01,
               -1.98062886e-03, -3.28251407e-03,  3.22106727e-02],
              [ 2.36709720e-01, -1.73959531e-02,  2.35395996e-01,
                8.15216826e-03, -1.51576124e-02,  3.92320180e-02]]])

    • omega_global_corr
      (chain, draw, omega_global_corr_dim_0, omega_global_corr_dim_1)
      float64
      1.0 0.9758 0.9179 ... 0.8284 1.0

      array([[[[1.        , 0.97584357, 0.91786403],
               [0.97584357, 1.        , 0.88564027],
               [0.91786403, 0.88564027, 1.        ]],
      
              [[1.        , 0.97406397, 0.92172696],
               [0.97406397, 1.        , 0.86207108],
               [0.92172696, 0.86207108, 1.        ]],
      
              [[1.        , 0.99057811, 0.94750053],
               [0.99057811, 1.        , 0.92594331],
               [0.94750053, 0.92594331, 1.        ]],
      
              ...,
      
              [[1.        , 0.9822147 , 0.89417307],
               [0.9822147 , 1.        , 0.86942173],
               [0.89417307, 0.86942173, 1.        ]],
      
              [[1.        , 0.98626896, 0.82152949],
               [0.98626896, 1.        , 0.79452495],
      ...
               [0.98561225, 1.        , 0.84898728],
               [0.87442717, 0.84898728, 1.        ]],
      
              [[1.        , 0.99838982, 0.88369556],
               [0.99838982, 1.        , 0.88125579],
               [0.88369556, 0.88125579, 1.        ]],
      
              ...,
      
              [[1.        , 0.98748604, 0.91956421],
               [0.98748604, 1.        , 0.88196208],
               [0.91956421, 0.88196208, 1.        ]],
      
              [[1.        , 0.99227684, 0.90690012],
               [0.99227684, 1.        , 0.87746611],
               [0.90690012, 0.87746611, 1.        ]],
      
              [[1.        , 0.97830934, 0.88055348],
               [0.97830934, 1.        , 0.82838574],
               [0.88055348, 0.82838574, 1.        ]]]])

    • omega_global_stds
      (chain, draw, omega_global_stds_dim_0)
      float64
      0.01219 0.0156 ... 0.01422 0.04844

      array([[[0.01218822, 0.0156033 , 0.04723232],
              [0.01083866, 0.01546581, 0.05127907],
              [0.01259793, 0.01521268, 0.04410727],
              ...,
              [0.01538368, 0.01430131, 0.05072532],
              [0.01742328, 0.01427676, 0.04982718],
              [0.01750076, 0.01530433, 0.05420601]],
      
             [[0.0096274 , 0.01486003, 0.04766759],
              [0.00911955, 0.01471251, 0.04570305],
              [0.01766926, 0.01352269, 0.04792088],
              ...,
              [0.01479791, 0.01377459, 0.04464239],
              [0.01378923, 0.01407682, 0.04411417],
              [0.01440868, 0.01338876, 0.04470281]],
      
             [[0.01858746, 0.01842537, 0.05731224],
              [0.01665598, 0.01728827, 0.05177552],
              [0.01536784, 0.01485824, 0.05005355],
              ...,
              [0.01309073, 0.01649988, 0.04592084],
              [0.0131297 , 0.01630005, 0.04572872],
              [0.00700433, 0.01726962, 0.05222457]],
      
             [[0.01657584, 0.0162293 , 0.04917841],
              [0.01429305, 0.01703056, 0.05451429],
              [0.01566869, 0.0154742 , 0.04950871],
              ...,
              [0.01586844, 0.01345838, 0.04789947],
              [0.01742985, 0.01462649, 0.04869647],
              [0.01696835, 0.01422226, 0.04843869]]])

    • betaX_Australia
      (chain, draw, betaX_Australia_dim_0, betaX_Australia_dim_1)
      float64
      0.006457 0.006665 ... 0.001335

      array([[[[ 6.45673426e-03,  6.66495929e-03,  9.63041308e-03],
               [ 6.16520826e-03,  5.35006929e-03,  7.47274676e-03],
               [ 6.20528768e-03,  7.28459069e-03,  8.09003561e-03],
               ...,
               [ 5.34834939e-03,  5.30224650e-03,  5.12230411e-03],
               [ 3.17715424e-03,  3.72264068e-03,  7.71014433e-03],
               [ 2.40968783e-03, -1.10769314e-04,  3.79703453e-03]],
      
              [[ 5.62247168e-03,  8.22585752e-03,  7.41526458e-03],
               [ 6.81212894e-03,  8.59259114e-03,  6.96929263e-03],
               [ 6.85824713e-03,  9.71421306e-03,  7.80050163e-03],
               ...,
               [ 5.27977559e-03,  7.12763087e-03,  7.85077320e-03],
               [ 2.26854670e-03,  4.17898849e-03,  1.99233690e-03],
               [ 6.99576361e-04,  8.41475757e-04,  3.12093505e-03]],
      
              [[ 6.03583532e-03,  8.91936376e-03,  8.55984040e-03],
               [ 6.28650722e-03,  9.56265653e-03,  7.12959851e-03],
               [ 6.99959099e-03,  1.08125186e-02,  8.21668424e-03],
               ...,
      ...
               ...,
               [ 2.38122422e-04,  7.08644246e-03, -3.15206342e-04],
               [ 1.90243108e-05,  7.41842090e-03, -8.50312926e-04],
               [ 2.38167305e-03,  2.04661747e-03,  3.32965871e-04]],
      
              [[-6.64125571e-04,  8.97977715e-03, -2.64531910e-03],
               [-1.04763537e-03,  8.47060066e-03, -1.53199568e-03],
               [-1.59438755e-03,  9.94896541e-03, -3.01275733e-03],
               ...,
               [-4.95738576e-04,  6.66240537e-03, -1.65050538e-03],
               [-4.20453564e-04,  5.68659459e-03, -1.80702263e-03],
               [ 2.19041506e-03,  1.42714757e-03,  9.97837296e-04]],
      
              [[ 4.91271171e-03,  7.32782997e-03, -9.03573280e-04],
               [ 4.09813289e-03,  6.55476026e-03,  1.86820033e-04],
               [ 3.98572968e-03,  7.12591868e-03, -6.45143885e-04],
               ...,
               [ 2.01519705e-03,  4.86064939e-03,  1.38575206e-03],
               [ 4.92548971e-03,  5.14889911e-03, -2.53475447e-03],
               [ 2.97291555e-03,  2.73004850e-03,  1.33470356e-03]]]])

    • noise_chol_Australia_corr
      (chain, draw, noise_chol_Australia_corr_dim_0, noise_chol_Australia_corr_dim_1)
      float64
      1.0 -0.54 0.2005 ... 0.08377 1.0

      array([[[[ 1.        , -0.53997105,  0.20050768],
               [-0.53997105,  1.        , -0.28020889],
               [ 0.20050768, -0.28020889,  1.        ]],
      
              [[ 1.        , -0.50379035, -0.09321638],
               [-0.50379035,  1.        ,  0.42466479],
               [-0.09321638,  0.42466479,  1.        ]],
      
              [[ 1.        , -0.44878606,  0.02712636],
               [-0.44878606,  1.        ,  0.14684738],
               [ 0.02712636,  0.14684738,  1.        ]],
      
              ...,
      
              [[ 1.        , -0.25046026, -0.00149379],
               [-0.25046026,  1.        ,  0.02489161],
               [-0.00149379,  0.02489161,  1.        ]],
      
              [[ 1.        , -0.54017118, -0.00869237],
               [-0.54017118,  1.        ,  0.15238841],
      ...
               [-0.63981809,  1.        ,  0.3501592 ],
               [-0.34526059,  0.3501592 ,  1.        ]],
      
              [[ 1.        , -0.4611995 ,  0.11083429],
               [-0.4611995 ,  1.        ,  0.06250126],
               [ 0.11083429,  0.06250126,  1.        ]],
      
              ...,
      
              [[ 1.        , -0.22836937,  0.18742943],
               [-0.22836937,  1.        , -0.1040565 ],
               [ 0.18742943, -0.1040565 ,  1.        ]],
      
              [[ 1.        , -0.30795064,  0.16498622],
               [-0.30795064,  1.        , -0.01919837],
               [ 0.16498622, -0.01919837,  1.        ]],
      
              [[ 1.        , -0.61568092,  0.23139218],
               [-0.61568092,  1.        ,  0.08377404],
               [ 0.23139218,  0.08377404,  1.        ]]]])

    • noise_chol_Australia_stds
      (chain, draw, noise_chol_Australia_stds_dim_0)
      float64
      0.175 0.4481 ... 0.3137 0.5729

      array([[[0.17500906, 0.44811006, 0.77881443],
              [0.32728677, 0.41040809, 0.94232891],
              [0.20737679, 0.4606506 , 0.95026555],
              ...,
              [0.0245075 , 0.40449207, 0.54958963],
              [0.08913057, 0.42739427, 0.34271204],
              [0.02162679, 0.32423213, 0.49410947]],
      
             [[0.18095635, 0.49858924, 0.80371497],
              [0.26401751, 0.60012323, 0.94142484],
              [0.03782971, 0.45779185, 0.79127935],
              ...,
              [0.11119029, 0.4450368 , 1.15437778],
              [0.08891332, 0.42875352, 1.25429922],
              [0.10683573, 0.45610541, 1.21426033]],
      
             [[0.05160502, 0.46142053, 0.82863923],
              [0.03275265, 0.40948387, 0.89037715],
              [0.01766209, 0.42345364, 0.59686582],
              ...,
              [0.27902307, 0.33740119, 1.19117012],
              [0.23885451, 0.36891792, 1.11060868],
              [0.28398386, 0.31559965, 0.79593116]],
      
             [[0.03881315, 0.51492137, 1.07699938],
              [0.05640983, 0.73044501, 0.41342372],
              [0.0950187 , 0.76513689, 1.14483558],
              ...,
              [0.0544019 , 0.38787546, 0.59211677],
              [0.11939583, 0.46289356, 0.68249328],
              [0.04304909, 0.31370608, 0.57285215]]])

    • omega_Australia
      (chain, draw, omega_Australia_dim_0, omega_Australia_dim_1)
      float64
      0.01645 0.0 ... -0.003485 0.03422

      array([[[[ 0.01645241,  0.        ,  0.        ],
               [ 0.00849064,  0.01319737,  0.        ],
               [ 0.04630716, -0.00628284,  0.0376755 ]],
      
              [[ 0.01776509,  0.        ,  0.        ],
               [ 0.01020939,  0.01118267,  0.        ],
               [ 0.0443081 ,  0.00109399,  0.03621514]],
      
              [[ 0.01704101,  0.        ,  0.        ],
               [ 0.01000982,  0.01142607,  0.        ],
               [ 0.04142636, -0.00011768,  0.03451845]],
      
              ...,
      
              [[ 0.01563076,  0.        ,  0.        ],
               [ 0.01092309,  0.0132171 ,  0.        ],
               [ 0.0441067 , -0.00194878,  0.03685126]],
      
              [[ 0.0193523 ,  0.        ,  0.        ],
               [ 0.00749132,  0.01197011,  0.        ],
      ...
               [ 0.00827159,  0.01269999,  0.        ],
               [ 0.04432031, -0.00285162,  0.03237427]],
      
              [[ 0.01694401,  0.        ,  0.        ],
               [ 0.00952946,  0.01177505,  0.        ],
               [ 0.0450868 ,  0.00148287,  0.04091808]],
      
              ...,
      
              [[ 0.01688243,  0.        ,  0.        ],
               [ 0.01060932,  0.0120037 ,  0.        ],
               [ 0.04580797, -0.00869739,  0.03189607]],
      
              [[ 0.02005698,  0.        ,  0.        ],
               [ 0.01046687,  0.0131143 ,  0.        ],
               [ 0.04592615, -0.00799437,  0.03538846]],
      
              [[ 0.01761159,  0.        ,  0.        ],
               [ 0.00880706,  0.00897023,  0.        ],
               [ 0.04487011, -0.00348537,  0.03421569]]]])

    • betaX_Canada
      (chain, draw, betaX_Canada_dim_0, betaX_Canada_dim_1)
      float64
      0.01247 0.003499 ... -0.004845

      array([[[[ 1.24700229e-02,  3.49888035e-03,  3.17631156e-03],
               [ 1.49572516e-02,  4.59849318e-03,  5.23948172e-03],
               [ 1.11409290e-02,  3.40311576e-03,  2.78466775e-03],
               ...,
               [ 9.42362534e-03,  3.02113378e-03,  4.26624859e-03],
               [ 6.09631303e-03,  2.33500972e-03,  3.17155501e-03],
               [-9.81937900e-03, -1.93179353e-03, -4.02832249e-03]],
      
              [[ 5.55326597e-03,  1.00136700e-02,  1.04013746e-02],
               [ 6.92007696e-03,  1.27153046e-02,  1.17002176e-02],
               [ 7.35928121e-03,  1.19274704e-02,  1.12212105e-02],
               ...,
               [ 4.08314668e-03,  8.75353028e-03,  6.65613365e-03],
               [ 2.43987976e-03,  5.95342126e-03,  4.05159400e-03],
               [ 1.05279891e-03, -2.47692220e-03, -3.40605712e-03]],
      
              [[ 7.65554518e-03,  5.41194263e-03,  9.54488372e-03],
               [ 9.15665658e-03,  6.88104456e-03,  1.11121618e-02],
               [ 6.89955222e-03,  7.08948466e-03,  9.77147290e-03],
               ...,
      ...
               ...,
               [ 2.45715187e-03,  5.19941214e-03,  4.34379533e-03],
               [ 1.35074050e-03,  4.05808015e-03,  3.73484744e-03],
               [-1.89123017e-03,  2.17836673e-03, -2.97893739e-04]],
      
              [[ 1.53180566e-03,  5.08215787e-03,  5.05360333e-03],
               [ 7.44626869e-04,  6.60363132e-03,  6.56758081e-03],
               [-2.40149387e-04,  7.51450347e-03,  5.22763736e-03],
               ...,
               [-3.34373481e-04,  5.14172725e-03,  4.62906142e-03],
               [-4.91254186e-04,  4.10078261e-03,  3.98687062e-03],
               [-3.50396455e-03,  3.47348333e-03, -9.08573735e-04]],
      
              [[ 5.34685825e-03,  1.25850786e-03,  5.32328941e-03],
               [ 5.91432977e-03,  1.19781114e-03,  7.31923031e-03],
               [ 6.34408641e-03,  1.90335124e-03,  5.12804004e-03],
               ...,
               [ 3.64558827e-03,  1.23370266e-03,  5.24797956e-03],
               [ 2.29374113e-03,  9.70973007e-04,  3.79256349e-03],
               [-2.35460757e-03,  8.93351321e-04, -4.84480591e-03]]]])

    • noise_chol_Canada_corr
      (chain, draw, noise_chol_Canada_corr_dim_0, noise_chol_Canada_corr_dim_1)
      float64
      1.0 0.1933 -0.2897 ... 0.07205 1.0

      array([[[[ 1.        ,  0.19328004, -0.28966389],
               [ 0.19328004,  1.        ,  0.05903915],
               [-0.28966389,  0.05903915,  1.        ]],
      
              [[ 1.        , -0.14078658, -0.3333484 ],
               [-0.14078658,  1.        ,  0.00109628],
               [-0.3333484 ,  0.00109628,  1.        ]],
      
              [[ 1.        , -0.17240732, -0.14634189],
               [-0.17240732,  1.        ,  0.14518812],
               [-0.14634189,  0.14518812,  1.        ]],
      
              ...,
      
              [[ 1.        ,  0.10648015,  0.03994961],
               [ 0.10648015,  1.        , -0.11973097],
               [ 0.03994961, -0.11973097,  1.        ]],
      
              [[ 1.        ,  0.09151256, -0.13585816],
               [ 0.09151256,  1.        , -0.00133437],
      ...
               [-0.14063703,  1.        , -0.28907142],
               [-0.24782725, -0.28907142,  1.        ]],
      
              [[ 1.        , -0.31655828, -0.25260422],
               [-0.31655828,  1.        , -0.11332257],
               [-0.25260422, -0.11332257,  1.        ]],
      
              ...,
      
              [[ 1.        ,  0.18083947,  0.13559932],
               [ 0.18083947,  1.        , -0.02197691],
               [ 0.13559932, -0.02197691,  1.        ]],
      
              [[ 1.        ,  0.12001937,  0.49667666],
               [ 0.12001937,  1.        , -0.06958886],
               [ 0.49667666, -0.06958886,  1.        ]],
      
              [[ 1.        ,  0.41050003,  0.22813931],
               [ 0.41050003,  1.        ,  0.07204544],
               [ 0.22813931,  0.07204544,  1.        ]]]])

    • noise_chol_Canada_stds
      (chain, draw, noise_chol_Canada_stds_dim_0)
      float64
      0.6638 0.2085 ... 0.2936 1.213

      array([[[0.66384179, 0.20848881, 1.07124732],
              [0.67223062, 0.33682297, 0.91232871],
              [0.45749913, 0.32345847, 0.70680997],
              ...,
              [0.23020835, 0.25749084, 0.50378472],
              [0.58347185, 0.27866043, 0.53718941],
              [0.18709708, 0.28383023, 0.13075696]],
      
             [[0.68952306, 0.38286238, 0.87263223],
              [0.55548121, 0.46889733, 0.80054282],
              [0.4537614 , 0.50888115, 0.86099929],
              ...,
              [0.34183028, 0.34435015, 1.81518733],
              [0.32059482, 0.41286674, 1.11077189],
              [0.3560867 , 0.40310915, 1.57082235]],
      
             [[0.24603132, 0.31396591, 0.69534941],
              [0.22170782, 0.28096809, 1.12813663],
              [0.43843064, 0.24032078, 0.673225  ],
              ...,
              [0.48539611, 0.23639078, 1.13485029],
              [0.34601336, 0.19702292, 1.21354531],
              [0.87289064, 0.21110788, 0.61522443]],
      
             [[0.54622309, 0.43593431, 0.28842257],
              [0.65717069, 0.46764966, 1.19080717],
              [0.27563122, 0.54788095, 1.05204099],
              ...,
              [0.4678951 , 0.30428817, 0.70838538],
              [0.60572859, 0.28596595, 0.530754  ],
              [0.35621336, 0.29360534, 1.21302601]]])

    • omega_Canada
      (chain, draw, omega_Canada_dim_0, omega_Canada_dim_1)
      float64
      0.02925 0.0 ... -0.008251 0.0502

      array([[[[ 2.92546585e-02,  0.00000000e+00,  0.00000000e+00],
               [ 1.58829560e-02,  8.67682572e-03,  0.00000000e+00],
               [ 3.40908404e-02,  1.17293320e-03,  4.47826285e-02]],
      
              [[ 2.53152303e-02,  0.00000000e+00,  0.00000000e+00],
               [ 1.36970189e-02,  1.07218602e-02,  0.00000000e+00],
               [ 3.95740937e-02, -8.84898064e-03,  3.65696665e-02]],
      
              [[ 2.27465270e-02,  0.00000000e+00,  0.00000000e+00],
               [ 1.34535147e-02,  9.30373197e-03,  0.00000000e+00],
               [ 3.84788893e-02, -2.01148218e-03,  2.90241723e-02]],
      
              ...,
      
              [[ 2.12011736e-02,  0.00000000e+00,  0.00000000e+00],
               [ 1.44090336e-02,  9.54577122e-03,  0.00000000e+00],
               [ 4.46739461e-02, -4.02683003e-03,  3.54981952e-02]],
      
              [[ 3.26507622e-02,  0.00000000e+00,  0.00000000e+00],
               [ 1.43879430e-02,  9.75922918e-03,  0.00000000e+00],
      ...
               [ 1.53337409e-02,  1.09701702e-02,  0.00000000e+00],
               [ 4.16406670e-02, -1.09259006e-02,  4.47574983e-02]],
      
              [[ 1.98468252e-02,  0.00000000e+00,  0.00000000e+00],
               [ 1.24135044e-02,  9.21640803e-03,  0.00000000e+00],
               [ 3.87763130e-02, -4.31859096e-03,  3.87772103e-02]],
      
              ...,
      
              [[ 2.77633495e-02,  0.00000000e+00,  0.00000000e+00],
               [ 1.43882668e-02,  9.94183087e-03,  0.00000000e+00],
               [ 4.54152589e-02, -8.59838307e-03,  3.50699796e-02]],
      
              [[ 3.25872062e-02,  0.00000000e+00,  0.00000000e+00],
               [ 1.50238703e-02,  9.08214401e-03,  0.00000000e+00],
               [ 4.98169093e-02, -1.03582216e-02,  2.97896361e-02]],
      
              [[ 2.53352789e-02,  0.00000000e+00,  0.00000000e+00],
               [ 1.65431644e-02,  9.47652540e-03,  0.00000000e+00],
               [ 4.84262120e-02, -8.25059215e-03,  5.02025697e-02]]]])

    • betaX_Chile
      (chain, draw, betaX_Chile_dim_0, betaX_Chile_dim_1)
      float64
      0.003003 0.006249 ... -0.00412

      array([[[[ 3.00269072e-03,  6.24872689e-03, -9.55016990e-03],
               [-1.45623997e-02, -1.55714871e-02, -1.23016029e-02],
               [-1.15056639e-02, -4.98474488e-03,  1.00142545e-03],
               ...,
               [ 4.40286270e-03,  4.21659692e-03,  1.41303914e-02],
               [ 5.24313848e-03,  7.20257637e-03,  1.33433018e-02],
               [-7.25214830e-03, -3.39585308e-03, -1.63731319e-02]],
      
              [[ 1.27507817e-03, -4.89803702e-03,  1.92256262e-02],
               [-1.83711084e-02, -3.44935006e-02,  2.77951318e-03],
               [-6.24431318e-03, -1.60618990e-02, -6.40851652e-03],
               ...,
               [-9.03231703e-04,  1.08382348e-03,  3.30209617e-03],
               [ 5.27233353e-03,  8.86824000e-03, -1.15353010e-03],
               [ 1.16659387e-03, -5.20195709e-03, -1.38509917e-03]],
      
              [[ 9.89307608e-03, -5.74165359e-03,  7.91040108e-03],
               [-1.67669462e-02, -2.86250498e-02,  1.03911369e-02],
               [-1.51037867e-02, -1.20229355e-02,  9.08907897e-04],
               ...,
      ...
               ...,
               [-3.17410948e-07,  2.70798475e-03, -3.10499155e-03],
               [ 4.83756910e-03,  8.73702776e-03, -1.32916332e-03],
               [ 2.82261443e-04, -4.07766714e-03,  2.72946005e-03]],
      
              [[-1.05686768e-02, -2.80749013e-04, -1.03762948e-02],
               [-1.13119168e-02, -1.58087903e-02, -9.68889878e-03],
               [ 4.31255971e-03, -4.63753719e-03, -7.59437674e-05],
               ...,
               [ 4.49659370e-04,  2.87217458e-03, -1.86698162e-03],
               [ 3.82583331e-03,  8.99343334e-03,  1.06381035e-03],
               [-1.51498565e-03, -1.39370685e-03, -7.91374858e-04]],
      
              [[-5.77579546e-03, -1.14072896e-02,  2.38413016e-03],
               [-6.83860672e-03, -2.46730317e-02, -9.11421479e-04],
               [-1.14180209e-03,  1.08306232e-03, -1.70201083e-03],
               ...,
               [ 3.07333793e-03,  1.78565109e-03,  6.40907518e-03],
               [ 4.86858088e-03,  6.20895393e-03,  7.98444814e-03],
               [-4.94152216e-03, -5.58138556e-03, -4.11992869e-03]]]])

    • noise_chol_Chile_corr
      (chain, draw, noise_chol_Chile_corr_dim_0, noise_chol_Chile_corr_dim_1)
      float64
      1.0 0.6129 0.3999 ... 0.5206 1.0

      array([[[[1.        , 0.61285411, 0.39987636],
               [0.61285411, 1.        , 0.09210604],
               [0.39987636, 0.09210604, 1.        ]],
      
              [[1.        , 0.50058186, 0.63135693],
               [0.50058186, 1.        , 0.36835608],
               [0.63135693, 0.36835608, 1.        ]],
      
              [[1.        , 0.57156141, 0.65836342],
               [0.57156141, 1.        , 0.3644959 ],
               [0.65836342, 0.3644959 , 1.        ]],
      
              ...,
      
              [[1.        , 0.61136954, 0.63824026],
               [0.61136954, 1.        , 0.26365707],
               [0.63824026, 0.26365707, 1.        ]],
      
              [[1.        , 0.55530727, 0.56335901],
               [0.55530727, 1.        , 0.27030894],
      ...
               [0.43938051, 1.        , 0.07429358],
               [0.62810518, 0.07429358, 1.        ]],
      
              [[1.        , 0.63697676, 0.5034427 ],
               [0.63697676, 1.        , 0.39377102],
               [0.5034427 , 0.39377102, 1.        ]],
      
              ...,
      
              [[1.        , 0.50260036, 0.27765771],
               [0.50260036, 1.        , 0.2654174 ],
               [0.27765771, 0.2654174 , 1.        ]],
      
              [[1.        , 0.59924247, 0.39082225],
               [0.59924247, 1.        , 0.31288678],
               [0.39082225, 0.31288678, 1.        ]],
      
              [[1.        , 0.59940686, 0.59922862],
               [0.59940686, 1.        , 0.52060502],
               [0.59922862, 0.52060502, 1.        ]]]])

    • noise_chol_Chile_stds
      (chain, draw, noise_chol_Chile_stds_dim_0)
      float64
      1.271 1.624 3.6 ... 1.68 2.743

      array([[[1.2713373 , 1.62414038, 3.59991746],
              [1.40839471, 1.64880118, 3.31877818],
              [1.05662488, 1.71732613, 3.42270954],
              ...,
              [1.02995934, 1.60248178, 2.69900726],
              [0.76983079, 1.4651506 , 2.20052647],
              [0.99565962, 1.60421725, 2.68589717]],
      
             [[0.91491713, 1.34253895, 2.2662561 ],
              [1.54426339, 2.00255192, 2.8945698 ],
              [1.27900868, 2.17221178, 3.52071618],
              ...,
              [0.80886664, 1.52772598, 2.89590313],
              [0.82952097, 1.32740011, 2.73284552],
              [0.79969338, 1.26148752, 2.85823385]],
      
             [[0.91773985, 1.56062253, 2.79411   ],
              [1.00685964, 1.2855223 , 2.78101382],
              [0.93764767, 1.47389141, 2.23833153],
              ...,
              [1.24101022, 1.8708186 , 3.69690198],
              [1.31056705, 1.81169217, 3.36838218],
              [1.07192233, 1.32214889, 2.47574968]],
      
             [[1.29850511, 2.08605599, 3.33642843],
              [1.52666923, 1.95601462, 3.53240985],
              [1.5267606 , 2.81179684, 3.85790135],
              ...,
              [0.87863276, 1.72022698, 2.82345444],
              [1.00752757, 1.40806588, 2.55055337],
              [0.84373496, 1.68048138, 2.74291593]]])

    • omega_Chile
      (chain, draw, omega_Chile_dim_0, omega_Chile_dim_1)
      float64
      0.04516 0.0 0.0 ... 0.006101 0.0735

      array([[[[ 0.04516462,  0.        ,  0.        ],
               [ 0.04089555,  0.03693081,  0.        ],
               [ 0.07991772, -0.02036609,  0.10259708]],
      
              [[ 0.04142842,  0.        ,  0.        ],
               [ 0.03280046,  0.03466477,  0.        ],
               [ 0.0920935 , -0.00353505,  0.07392714]],
      
              [[ 0.03641313,  0.        ,  0.        ],
               [ 0.03711581,  0.03418023,  0.        ],
               [ 0.09224015, -0.00509764,  0.07195252]],
      
              ...,
      
              [[ 0.04285858,  0.        ,  0.        ],
               [ 0.04019725,  0.03695334,  0.        ],
               [ 0.09077766, -0.01401341,  0.07701291]],
      
              [[ 0.03766407,  0.        ,  0.        ],
               [ 0.03558912,  0.03507327,  0.        ],
      ...
               [ 0.03160417,  0.03372773,  0.        ],
               [ 0.08584851, -0.01802142,  0.07194311]],
      
              [[ 0.03995506,  0.        ,  0.        ],
               [ 0.04398685,  0.03570095,  0.        ],
               [ 0.07426316,  0.0050056 ,  0.07603408]],
      
              ...,
      
              [[ 0.03857175,  0.        ,  0.        ],
               [ 0.03569151,  0.0412009 ,  0.        ],
               [ 0.06351702,  0.00310009,  0.0871746 ]],
      
              [[ 0.04293945,  0.        ,  0.        ],
               [ 0.03587916,  0.0308109 ,  0.        ],
               [ 0.0687076 , -0.00211939,  0.07819696]],
      
              [[ 0.03735921,  0.        ,  0.        ],
               [ 0.03841383,  0.03604897,  0.        ],
               [ 0.08213845,  0.00610096,  0.07349513]]]])

    • betaX_Ireland
      (chain, draw, betaX_Ireland_dim_0, betaX_Ireland_dim_1)
      float64
      0.01648 0.01726 ... -0.02733

      array([[[[ 1.64836620e-02,  1.72578353e-02,  1.64182659e-02],
               [ 2.43504450e-02,  1.84689416e-02,  2.00754020e-02],
               [ 7.33619607e-03,  1.19017325e-02,  1.36770851e-02],
               ...,
               [-5.87607967e-04,  3.44866967e-03,  1.11521468e-02],
               [ 5.30266531e-02,  2.36051004e-02,  2.24552156e-02],
               [ 2.51764667e-02,  4.21411050e-02,  2.89011406e-02]],
      
              [[ 7.82774644e-03,  1.64443423e-02,  2.36731975e-02],
               [ 1.12804312e-02,  1.05602182e-02,  3.44037527e-02],
               [ 1.07559303e-02,  2.75232881e-02,  1.71403673e-03],
               ...,
               [-4.51099742e-03,  1.96146605e-02,  5.70295261e-03],
               [ 1.80841877e-02, -3.41386122e-02,  8.59956360e-02],
               [ 5.61955592e-02,  6.12612971e-02, -6.26802772e-03]],
      
              [[ 1.74751828e-02,  2.86672623e-02,  1.74833159e-02],
               [ 1.88330456e-02,  2.82139302e-02,  2.75691533e-02],
               [ 1.47183887e-02,  3.21766449e-02, -1.83083612e-02],
               ...,
      ...
               ...,
               [-9.91041283e-03,  1.85968541e-02,  6.60602392e-03],
               [ 1.13933117e-02,  2.35398549e-03, -1.07360996e-02],
               [ 4.99000324e-02,  7.04399668e-02, -7.62368101e-02]],
      
              [[ 6.18025714e-04,  1.83210873e-02,  6.20114060e-03],
               [ 4.27276181e-03,  1.68986884e-02,  6.71994714e-03],
               [ 7.43417339e-04,  2.81270925e-02,  4.19910060e-03],
               ...,
               [-1.38228245e-02,  1.97494034e-02,  1.53752579e-02],
               [ 1.83463571e-02, -2.04016832e-02,  8.62400171e-03],
               [ 4.52241270e-02,  5.87861112e-02, -3.03262169e-02]],
      
              [[ 7.46063846e-03,  2.43506583e-02, -5.49236629e-03],
               [ 7.99655643e-03,  1.88982657e-02, -5.19542351e-03],
               [ 5.77313098e-03,  3.52912201e-02, -4.08544848e-03],
               ...,
               [-1.18675129e-02,  2.35309218e-02, -2.47016723e-03],
               [ 1.33567965e-02, -2.49183450e-02,  1.01166132e-03],
               [ 6.59684494e-02,  8.88266272e-02, -2.73254140e-02]]]])

    • noise_chol_Ireland_corr
      (chain, draw, noise_chol_Ireland_corr_dim_0, noise_chol_Ireland_corr_dim_1)
      float64
      1.0 0.03333 0.2175 ... 0.2948 1.0

      array([[[[ 1.00000000e+00,  3.33342673e-02,  2.17495962e-01],
               [ 3.33342673e-02,  1.00000000e+00,  1.50420841e-01],
               [ 2.17495962e-01,  1.50420841e-01,  1.00000000e+00]],
      
              [[ 1.00000000e+00, -2.59961345e-01, -1.83604558e-01],
               [-2.59961345e-01,  1.00000000e+00,  5.43763057e-01],
               [-1.83604558e-01,  5.43763057e-01,  1.00000000e+00]],
      
              [[ 1.00000000e+00, -2.24535655e-01,  2.27162374e-02],
               [-2.24535655e-01,  1.00000000e+00,  3.68930801e-01],
               [ 2.27162374e-02,  3.68930801e-01,  1.00000000e+00]],
      
              ...,
      
              [[ 1.00000000e+00,  7.84638734e-03,  2.52670685e-01],
               [ 7.84638734e-03,  1.00000000e+00,  2.25266813e-01],
               [ 2.52670685e-01,  2.25266813e-01,  1.00000000e+00]],
      
              [[ 1.00000000e+00,  5.42195183e-02,  1.39904599e-01],
               [ 5.42195183e-02,  1.00000000e+00,  1.33651491e-01],
      ...
               [-2.49106507e-01,  1.00000000e+00,  1.60642213e-01],
               [ 2.49916275e-01,  1.60642213e-01,  1.00000000e+00]],
      
              [[ 1.00000000e+00,  4.35927922e-02,  1.08673539e-02],
               [ 4.35927922e-02,  1.00000000e+00,  2.08335723e-01],
               [ 1.08673539e-02,  2.08335723e-01,  1.00000000e+00]],
      
              ...,
      
              [[ 1.00000000e+00, -1.43199383e-01,  1.28602749e-01],
               [-1.43199383e-01,  1.00000000e+00,  2.40435719e-01],
               [ 1.28602749e-01,  2.40435719e-01,  1.00000000e+00]],
      
              [[ 1.00000000e+00, -3.92398800e-02,  1.54895511e-01],
               [-3.92398800e-02,  1.00000000e+00,  3.18864917e-01],
               [ 1.54895511e-01,  3.18864917e-01,  1.00000000e+00]],
      
              [[ 1.00000000e+00, -7.61891204e-02,  8.96321521e-02],
               [-7.61891204e-02,  1.00000000e+00,  2.94752950e-01],
               [ 8.96321521e-02,  2.94752950e-01,  1.00000000e+00]]]])

    • noise_chol_Ireland_stds
      (chain, draw, noise_chol_Ireland_stds_dim_0)
      float64
      1.099 0.889 5.445 ... 0.7554 5.359

      array([[[1.09856315, 0.88901252, 5.44525567],
              [1.07918067, 0.79173747, 6.35467293],
              [1.24444094, 0.90287933, 6.77229604],
              ...,
              [1.11717345, 0.73017693, 4.38263384],
              [0.79322542, 0.73202497, 5.07505363],
              [0.79691695, 0.75875025, 4.36341961]],
      
             [[1.20283767, 0.54777345, 4.65362658],
              [1.53763364, 0.75642027, 5.81766776],
              [1.16328075, 0.93651123, 5.99160043],
              ...,
              [1.25065627, 0.71665283, 6.28527513],
              [1.2169064 , 0.75343536, 5.39141314],
              [1.17824027, 0.6533815 , 4.65254295]],
      
             [[0.75713346, 0.68163394, 4.42842643],
              [0.70207832, 0.67130676, 5.78454619],
              [1.0214115 , 0.66706679, 4.34632939],
              ...,
              [1.30702197, 0.89851183, 6.58625894],
              [1.40896661, 0.88093035, 6.78873108],
              [0.90044203, 0.64658868, 4.13419835]],
      
             [[1.18230319, 1.19215547, 6.00616917],
              [1.6018197 , 1.28117501, 7.68278202],
              [1.84183924, 1.28813938, 7.38414326],
              ...,
              [0.74949096, 0.81424938, 4.41888313],
              [0.97737268, 0.86168422, 4.74508525],
              [0.85502325, 0.75541657, 5.35855291]]])

    • omega_Ireland
      (chain, draw, omega_Ireland_dim_0, omega_Ireland_dim_1)
      float64
      0.04064 0.0 0.0 ... 0.03243 0.1465

      array([[[[ 0.04063976,  0.        ,  0.        ],
               [ 0.01560372,  0.02658937,  0.        ],
               [ 0.07323416,  0.0183125 ,  0.15581926]],
      
              [[ 0.03422257,  0.        ,  0.        ],
               [ 0.01022993,  0.02015667,  0.        ],
               [ 0.02069296,  0.06352592,  0.13433755]],
      
              [[ 0.04069738,  0.        ,  0.        ],
               [ 0.01010118,  0.02210544,  0.        ],
               [ 0.04434761,  0.05532029,  0.15580224]],
      
              ...,
      
              [[ 0.04522035,  0.        ,  0.        ],
               [ 0.01382171,  0.02238523,  0.        ],
               [ 0.07411653,  0.02417507,  0.13370487]],
      
              [[ 0.03829342,  0.        ,  0.        ],
               [ 0.01476965,  0.02195785,  0.        ],
      ...
               [ 0.01087785,  0.02464814,  0.        ],
               [ 0.08059611,  0.0270211 ,  0.1527325 ]],
      
              [[ 0.04501903,  0.        ,  0.        ],
               [ 0.01610349,  0.02154706,  0.        ],
               [ 0.04433719,  0.02381899,  0.13885813]],
      
              ...,
      
              [[ 0.03517344,  0.        ,  0.        ],
               [ 0.00987196,  0.02327246,  0.        ],
               [ 0.05784165,  0.02269594,  0.12785515]],
      
              [[ 0.04216251,  0.        ,  0.        ],
               [ 0.01326842,  0.02395153,  0.        ],
               [ 0.06196187,  0.0311782 ,  0.13210447]],
      
              [[ 0.03763762,  0.        ,  0.        ],
               [ 0.01215112,  0.02145044,  0.        ],
               [ 0.05344668,  0.03243153,  0.1464945 ]]]])

    • betaX_New Zealand
      (chain, draw, betaX_New Zealand_dim_0, betaX_New Zealand_dim_1)
      float64
      -0.001764 0.001355 ... -0.001023

      array([[[[-1.76372364e-03,  1.35525819e-03,  2.02611146e-03],
               [ 1.76226292e-03, -1.40595699e-03, -7.01848911e-04],
               [ 6.77369237e-03,  9.44922545e-03,  7.84322633e-03],
               ...,
               [ 7.25825653e-03,  1.47405243e-02,  9.98505146e-03],
               [ 6.96508463e-03,  1.52436204e-02,  1.07166853e-02],
               [ 5.39886989e-03,  1.24515738e-02,  8.74174581e-03]],
      
              [[-7.33507167e-04, -1.98169808e-03, -5.63322918e-03],
               [ 5.34343160e-03,  1.49920196e-03,  4.23808747e-03],
               [ 1.00199291e-02,  1.06386052e-02,  1.78459333e-02],
               ...,
               [ 6.39741247e-03,  1.02239745e-02,  1.15700503e-02],
               [ 4.58740417e-03,  1.02182004e-02,  1.05329555e-02],
               [ 2.88523371e-03,  7.76261089e-03,  7.10482735e-03]],
      
              [[-3.29875020e-03, -3.50267944e-03, -4.86952563e-04],
               [ 7.27952619e-03,  7.06963951e-04, -5.50758663e-03],
               [ 1.58605090e-02,  1.32553477e-02,  7.81357852e-03],
               ...,
      ...
               ...,
               [ 3.10420929e-03,  7.87559969e-03,  7.96009257e-03],
               [ 2.86378859e-03,  8.30486587e-03,  6.22048805e-03],
               [ 1.63544841e-03,  6.62238454e-03,  4.42948689e-03]],
      
              [[-1.30996446e-03,  1.55487298e-03, -2.08606111e-03],
               [ 1.73072691e-03, -1.71345519e-03,  5.93278825e-03],
               [ 6.49868797e-03,  8.14610668e-03,  7.72636310e-03],
               ...,
               [ 1.57982970e-03,  1.00528358e-02,  4.64339627e-03],
               [ 1.46055332e-03,  1.11614280e-02,  2.42898064e-03],
               [ 2.51884702e-04,  9.01327227e-03,  1.40423677e-03]],
      
              [[-1.66947133e-03,  4.49148200e-03,  7.98465719e-06],
               [ 2.45136274e-03, -1.83504208e-03,  1.50542664e-03],
               [ 2.43912078e-03,  1.75038892e-03, -1.34805785e-03],
               ...,
               [ 1.25911370e-03,  6.16133924e-03,  1.04761826e-04],
               [ 8.44121536e-04,  6.76096491e-03, -1.54309646e-03],
               [ 2.94218980e-04,  6.08009144e-03, -1.02344794e-03]]]])

    • noise_chol_New Zealand_corr
      (chain, draw, noise_chol_New Zealand_corr_dim_0, noise_chol_New Zealand_corr_dim_1)
      float64
      1.0 -0.261 0.1799 ... 0.1502 1.0

      array([[[[ 1.        , -0.26103948,  0.1799095 ],
               [-0.26103948,  1.        ,  0.18151346],
               [ 0.1799095 ,  0.18151346,  1.        ]],
      
              [[ 1.        , -0.08742612,  0.11463748],
               [-0.08742612,  1.        , -0.2364093 ],
               [ 0.11463748, -0.2364093 ,  1.        ]],
      
              [[ 1.        , -0.28301592,  0.00105696],
               [-0.28301592,  1.        , -0.2199193 ],
               [ 0.00105696, -0.2199193 ,  1.        ]],
      
              ...,
      
              [[ 1.        , -0.20290854,  0.05859711],
               [-0.20290854,  1.        , -0.01508477],
               [ 0.05859711, -0.01508477,  1.        ]],
      
              [[ 1.        ,  0.01844096,  0.35830256],
               [ 0.01844096,  1.        , -0.07586697],
      ...
               [-0.37043066,  1.        ,  0.28849878],
               [ 0.29637054,  0.28849878,  1.        ]],
      
              [[ 1.        , -0.43535589,  0.00774529],
               [-0.43535589,  1.        , -0.15615354],
               [ 0.00774529, -0.15615354,  1.        ]],
      
              ...,
      
              [[ 1.        , -0.41551535,  0.33174242],
               [-0.41551535,  1.        ,  0.04805351],
               [ 0.33174242,  0.04805351,  1.        ]],
      
              [[ 1.        , -0.25748007,  0.27593397],
               [-0.25748007,  1.        ,  0.13310236],
               [ 0.27593397,  0.13310236,  1.        ]],
      
              [[ 1.        , -0.19664719,  0.36554005],
               [-0.19664719,  1.        ,  0.150203  ],
               [ 0.36554005,  0.150203  ,  1.        ]]]])

    • noise_chol_New Zealand_stds
      (chain, draw, noise_chol_New Zealand_stds_dim_0)
      float64
      0.3045 0.2385 1.12 ... 0.4065 1.071

      array([[[3.04534370e-01, 2.38521201e-01, 1.12038400e+00],
              [3.82169968e-01, 4.65253294e-01, 1.29437459e+00],
              [2.55826468e-01, 3.67222498e-01, 1.37690664e+00],
              ...,
              [2.05796473e-01, 2.78469568e-01, 1.01595357e+00],
              [4.82275138e-02, 3.52312849e-01, 8.60660486e-01],
              [9.96422216e-02, 3.18282233e-01, 7.08427063e-01]],
      
             [[2.96598158e-01, 2.81750195e-01, 1.23858942e+00],
              [3.68460688e-01, 2.85802825e-01, 1.58625384e+00],
              [2.66135207e-02, 3.33540996e-01, 1.48833319e+00],
              ...,
              [2.42703239e-01, 4.22863294e-01, 1.62550222e+00],
              [1.68752066e-01, 4.14486419e-01, 1.42264760e+00],
              [2.26454537e-01, 4.29511347e-01, 1.29795254e+00]],
      
             [[1.00180477e-01, 4.77008616e-01, 7.48245655e-01],
              [1.34293327e-01, 3.61395761e-01, 9.26934975e-01],
              [4.37944414e-02, 4.28662914e-01, 9.59362065e-01],
              ...,
              [3.26785762e-01, 3.03852946e-01, 1.32595851e+00],
              [2.97884495e-01, 3.53191395e-01, 1.37299126e+00],
              [3.22936817e-01, 3.53322178e-01, 1.03226229e+00]],
      
             [[1.13775785e-01, 4.77763837e-01, 9.55470465e-01],
              [1.42230904e-01, 4.41212942e-01, 9.87938056e-01],
              [7.12239451e-02, 6.48104937e-01, 1.15193371e+00],
              ...,
              [3.32437466e-03, 3.30767916e-01, 1.49072766e+00],
              [3.17245931e-03, 3.10529148e-01, 1.13832807e+00],
              [1.14414877e-03, 4.06543350e-01, 1.07140500e+00]]])

    • omega_New Zealand
      (chain, draw, omega_New Zealand_dim_0, omega_New Zealand_dim_1)
      float64
      0.01984 0.0 ... -0.001556 0.04494

      array([[[[ 0.0198446 ,  0.        ,  0.        ],
               [ 0.01319696,  0.00934973,  0.        ],
               [ 0.04749641,  0.00482864,  0.04614774]],
      
              [[ 0.01896637,  0.        ,  0.        ],
               [ 0.01384465,  0.01356738,  0.        ],
               [ 0.04947859, -0.01436299,  0.04516365]],
      
              [[ 0.01814619,  0.        ,  0.        ],
               [ 0.01235487,  0.01007004,  0.        ],
               [ 0.04087155, -0.01116694,  0.04377006]],
      
              ...,
      
              [[ 0.0205401 ,  0.        ,  0.        ],
               [ 0.01213642,  0.00999665,  0.        ],
               [ 0.04574107, -0.00241545,  0.04943785]],
      
              [[ 0.01825196,  0.        ,  0.        ],
               [ 0.01387671,  0.01177042,  0.        ],
      ...
               [ 0.01361614,  0.01003502,  0.        ],
               [ 0.05197953,  0.00337521,  0.04048826]],
      
              [[ 0.01656158,  0.        ,  0.        ],
               [ 0.01066615,  0.01024111,  0.        ],
               [ 0.04319086, -0.0040152 ,  0.04102882]],
      
              ...,
      
              [[ 0.01553835,  0.        ,  0.        ],
               [ 0.00932359,  0.00998369,  0.        ],
               [ 0.05590114,  0.00030017,  0.05274987]],
      
              [[ 0.01706251,  0.        ,  0.        ],
               [ 0.01207957,  0.00949851,  0.        ],
               [ 0.05111778, -0.00238222,  0.04555566]],
      
              [[ 0.01657807,  0.        ,  0.        ],
               [ 0.01159888,  0.01270442,  0.        ],
               [ 0.0512601 , -0.00155637,  0.04493924]]]])

    • betaX_South Africa
      (chain, draw, betaX_South Africa_dim_0, betaX_South Africa_dim_1)
      float64
      0.004925 0.01035 ... -0.002743

      array([[[[ 4.92477337e-03,  1.03488014e-02,  1.67717620e-02],
               [ 4.32435160e-03,  3.91730303e-03,  2.67024819e-02],
               [ 5.85941669e-03,  6.08892086e-03,  2.71249215e-02],
               ...,
               [ 2.00654636e-03,  2.83766727e-04,  5.68007915e-03],
               [ 2.14998996e-03,  2.16766524e-03,  2.38793085e-03],
               [ 2.76682380e-03,  4.27981426e-03, -3.05339838e-02]],
      
              [[-4.97662591e-04,  7.41471039e-03,  6.69020614e-03],
               [ 1.16834788e-03,  9.77819530e-03,  4.29382253e-03],
               [ 1.79620485e-03,  1.38927964e-02,  8.00042377e-03],
               ...,
               [-4.88999869e-04,  4.77078413e-03, -1.05815533e-03],
               [-1.16997372e-03,  3.69873336e-03, -1.39553035e-03],
               [-9.53720437e-03, -5.05125885e-03, -1.18212411e-02]],
      
              [[ 1.71251393e-03,  7.07095518e-03,  6.18888899e-03],
               [ 3.40542884e-04,  5.58770770e-03,  7.12103121e-03],
               [ 8.01976717e-04,  8.98069910e-03,  8.92572794e-03],
               ...,
      ...
               ...,
               [ 1.15226380e-03,  1.91149281e-03, -4.87228787e-04],
               [ 1.64967287e-03,  2.09344683e-03, -2.42887920e-03],
               [ 8.08280694e-03,  4.38379543e-03, -2.61536007e-02]],
      
              [[ 3.51350470e-03,  5.16306728e-03,  1.14478061e-02],
               [ 3.32474240e-03,  4.46254142e-03,  1.24576395e-02],
               [ 4.36563776e-03,  6.23398176e-03,  1.55351359e-02],
               ...,
               [ 1.98228326e-03,  2.71357226e-03,  5.54662649e-04],
               [ 2.03929097e-03,  3.03869428e-03, -7.55485240e-04],
               [ 3.60510920e-03,  3.55289045e-03, -2.17092809e-02]],
      
              [[ 2.11524685e-03,  7.40829954e-03,  5.40311009e-03],
               [-1.12407675e-03,  4.43711011e-03,  4.67768445e-03],
               [ 5.60675386e-04,  4.52186968e-03,  4.46295420e-03],
               ...,
               [ 1.26343689e-03, -1.79230279e-05, -5.60797573e-04],
               [ 2.33385298e-03,  4.07356663e-04, -5.71025786e-04],
               [ 9.04329474e-03,  2.78928006e-03, -2.74255936e-03]]]])

    • noise_chol_South Africa_corr
      (chain, draw, noise_chol_South Africa_corr_dim_0, noise_chol_South Africa_corr_dim_1)
      float64
      1.0 0.3134 0.3718 ... 0.3246 1.0

      array([[[[ 1.        ,  0.31340689,  0.37177584],
               [ 0.31340689,  1.        ,  0.07821922],
               [ 0.37177584,  0.07821922,  1.        ]],
      
              [[ 1.        ,  0.21585394, -0.01498537],
               [ 0.21585394,  1.        ,  0.49303792],
               [-0.01498537,  0.49303792,  1.        ]],
      
              [[ 1.        ,  0.31726026,  0.00430444],
               [ 0.31726026,  1.        ,  0.23973121],
               [ 0.00430444,  0.23973121,  1.        ]],
      
              ...,
      
              [[ 1.        ,  0.2982329 ,  0.07047868],
               [ 0.2982329 ,  1.        ,  0.28969585],
               [ 0.07047868,  0.28969585,  1.        ]],
      
              [[ 1.        ,  0.48468315,  0.1270014 ],
               [ 0.48468315,  1.        ,  0.23816423],
      ...
               [ 0.36848594,  1.        ,  0.20173571],
               [ 0.15172166,  0.20173571,  1.        ]],
      
              [[ 1.        , -0.09939339, -0.09001966],
               [-0.09939339,  1.        ,  0.246294  ],
               [-0.09001966,  0.246294  ,  1.        ]],
      
              ...,
      
              [[ 1.        ,  0.49192847,  0.15722143],
               [ 0.49192847,  1.        ,  0.29030496],
               [ 0.15722143,  0.29030496,  1.        ]],
      
              [[ 1.        ,  0.40425884,  0.16604949],
               [ 0.40425884,  1.        ,  0.31644025],
               [ 0.16604949,  0.31644025,  1.        ]],
      
              [[ 1.        ,  0.71214665,  0.22512108],
               [ 0.71214665,  1.        ,  0.32460632],
               [ 0.22512108,  0.32460632,  1.        ]]]])

    • noise_chol_South Africa_stds
      (chain, draw, noise_chol_South Africa_stds_dim_0)
      float64
      0.5349 0.431 1.158 ... 0.4302 1.215

      array([[[0.53491119, 0.43096338, 1.15824286],
              [0.45006859, 0.35684383, 1.5885366 ],
              [0.52911664, 0.43826098, 1.76829858],
              ...,
              [0.23929478, 0.30540305, 1.50599346],
              [0.14620517, 0.45102983, 0.76363429],
              [0.28107478, 0.34724727, 1.15130411]],
      
             [[0.49119883, 0.35511895, 1.2359541 ],
              [0.49160659, 0.37286036, 0.95768854],
              [0.25065236, 0.50137585, 1.59148099],
              ...,
              [0.30518656, 0.53886371, 1.78000421],
              [0.33670211, 0.38883329, 1.66176677],
              [0.27916421, 0.49112526, 2.23205404]],
      
             [[0.18622751, 0.30379024, 1.47280193],
              [0.2317029 , 0.33054694, 1.06820261],
              [0.33985707, 0.35578534, 1.58447067],
              ...,
              [0.40043675, 0.38138817, 1.58591225],
              [0.43754413, 0.38519242, 1.48266707],
              [0.50844278, 0.29928312, 1.03343328]],
      
             [[0.26213754, 0.42430145, 1.13051579],
              [0.51324612, 0.52382017, 1.03951709],
              [0.26241434, 0.6543379 , 1.67900713],
              ...,
              [0.30151799, 0.61119872, 1.00398122],
              [0.29867705, 0.69957259, 0.8696062 ],
              [0.38222619, 0.43017794, 1.21473577]]])

    • omega_South Africa
      (chain, draw, omega_South Africa_dim_0, omega_South Africa_dim_1)
      float64
      0.02588 0.0 ... -0.0005307 0.04942

      array([[[[ 0.02587804,  0.        ,  0.        ],
               [ 0.01836493,  0.01403763,  0.        ],
               [ 0.05349481, -0.00333952,  0.04626514]],
      
              [[ 0.02045254,  0.        ,  0.        ],
               [ 0.0164209 ,  0.01104938,  0.        ],
               [ 0.04570972,  0.00974748,  0.04770504]],
      
              [[ 0.02438019,  0.        ,  0.        ],
               [ 0.01789729,  0.0115165 ,  0.        ],
               [ 0.04101198,  0.00616365,  0.05223724]],
      
              ...,
      
              [[ 0.02144724,  0.        ,  0.        ],
               [ 0.01613305,  0.01050653,  0.        ],
               [ 0.04700323,  0.00915405,  0.06100091]],
      
              [[ 0.02088769,  0.        ,  0.        ],
               [ 0.01958275,  0.01290723,  0.        ],
      ...
               [ 0.01988475,  0.01139151,  0.        ],
               [ 0.04960407, -0.00120676,  0.04350152]],
      
              [[ 0.0196344 ,  0.        ,  0.        ],
               [ 0.01415571,  0.01132816,  0.        ],
               [ 0.04061827,  0.00556347,  0.04887737]],
      
              ...,
      
              [[ 0.0233852 ,  0.        ,  0.        ],
               [ 0.02085216,  0.01606946,  0.        ],
               [ 0.04704126, -0.00125472,  0.04190013]],
      
              [[ 0.02467611,  0.        ,  0.        ],
               [ 0.02142607,  0.01825339,  0.        ],
               [ 0.04674536, -0.0024714 ,  0.03928832]],
      
              [[ 0.02597684,  0.        ,  0.        ],
               [ 0.02112623,  0.01032176,  0.        ],
               [ 0.04834541, -0.0005307 ,  0.04941882]]]])

    • betaX_United Kingdom
      (chain, draw, betaX_United Kingdom_dim_0, betaX_United Kingdom_dim_1)
      float64
      0.006215 0.007962 ... -0.0008488

      array([[[[ 6.21527654e-03,  7.96242658e-03,  7.88051157e-03],
               [ 1.15171077e-02,  1.16361614e-02,  1.48235468e-02],
               [ 1.60614500e-03,  4.64278585e-03,  5.09645397e-03],
               ...,
               [ 3.11837065e-03,  4.52830660e-03,  3.85966222e-03],
               [ 2.72398143e-03,  3.12844071e-03,  3.78236467e-03],
               [-1.34696113e-02, -1.24753844e-02, -1.27756146e-02]],
      
              [[ 4.57886040e-03,  7.46487033e-03,  6.37450381e-03],
               [ 6.72372630e-03,  9.75144856e-03,  4.85785417e-03],
               [-2.40024310e-03,  9.83485240e-03,  3.45607862e-03],
               ...,
               [ 2.18882061e-03,  4.62963920e-03,  4.21873249e-03],
               [ 1.49583464e-03,  3.17624696e-03,  1.53531195e-03],
               [-1.32462642e-02, -2.22963646e-03, -9.45690105e-03]],
      
              [[ 3.05786456e-03,  5.72964323e-03,  1.41988294e-02],
               [ 3.84512745e-03,  8.16457708e-03,  1.99662356e-02],
               [ 5.74171450e-03,  7.84849071e-03,  7.32288675e-03],
               ...,
      ...
               ...,
               [ 2.63601200e-04,  9.58823988e-04,  2.74848285e-03],
               [ 4.17599347e-04,  8.03252204e-04,  2.32558242e-03],
               [-9.59425164e-04, -7.43012309e-03, -8.41686030e-03]],
      
              [[ 1.00242066e-03,  4.81168942e-04,  5.58231368e-03],
               [-4.21113612e-04,  1.20499479e-03,  6.14387145e-03],
               [ 2.62728541e-04,  1.78384078e-03,  3.48250277e-03],
               ...,
               [-5.73395517e-04,  5.29181893e-04,  3.16248307e-03],
               [ 5.72243946e-04,  2.23936860e-04,  1.89344881e-03],
               [ 2.17874407e-03, -3.72872663e-04, -7.26549941e-03]],
      
              [[ 1.71332328e-03,  2.29020264e-03,  2.69870951e-03],
               [ 1.99736573e-03,  5.71654164e-03,  5.37697455e-03],
               [-1.16874867e-03,  8.01736567e-03,  3.20344007e-03],
               ...,
               [-2.77691368e-04,  1.60241469e-03,  1.46174472e-03],
               [ 9.20442780e-04,  1.73041839e-03,  1.53158472e-03],
               [-2.73090553e-03,  4.47796455e-03, -8.48761300e-04]]]])

    • noise_chol_United Kingdom_corr
      (chain, draw, noise_chol_United Kingdom_corr_dim_0, noise_chol_United Kingdom_corr_dim_1)
      float64
      1.0 0.5468 -0.08382 ... -0.3961 1.0

      array([[[[ 1.        ,  0.54681343, -0.08381696],
               [ 0.54681343,  1.        , -0.08092586],
               [-0.08381696, -0.08092586,  1.        ]],
      
              [[ 1.        ,  0.53047327, -0.21048533],
               [ 0.53047327,  1.        , -0.07649641],
               [-0.21048533, -0.07649641,  1.        ]],
      
              [[ 1.        ,  0.21884439, -0.30994369],
               [ 0.21884439,  1.        ,  0.00211945],
               [-0.30994369,  0.00211945,  1.        ]],
      
              ...,
      
              [[ 1.        ,  0.61098734, -0.15671942],
               [ 0.61098734,  1.        , -0.04346526],
               [-0.15671942, -0.04346526,  1.        ]],
      
              [[ 1.        ,  0.43507977, -0.15288278],
               [ 0.43507977,  1.        , -0.12857772],
      ...
               [ 0.45357421,  1.        , -0.10553591],
               [-0.25567594, -0.10553591,  1.        ]],
      
              [[ 1.        ,  0.27843166, -0.14093499],
               [ 0.27843166,  1.        , -0.15293376],
               [-0.14093499, -0.15293376,  1.        ]],
      
              ...,
      
              [[ 1.        ,  0.49718739, -0.10810989],
               [ 0.49718739,  1.        ,  0.1261408 ],
               [-0.10810989,  0.1261408 ,  1.        ]],
      
              [[ 1.        ,  0.37601611, -0.12683991],
               [ 0.37601611,  1.        ,  0.10034105],
               [-0.12683991,  0.10034105,  1.        ]],
      
              [[ 1.        ,  0.67810689, -0.11132734],
               [ 0.67810689,  1.        , -0.39613488],
               [-0.11132734, -0.39613488,  1.        ]]]])

    • noise_chol_United Kingdom_stds
      (chain, draw, noise_chol_United Kingdom_stds_dim_0)
      float64
      0.5181 0.3656 ... 0.502 0.3273

      array([[[0.51805797, 0.36561912, 0.41219843],
              [0.68063806, 0.3258411 , 0.64850899],
              [0.51016555, 0.36411294, 0.61003021],
              ...,
              [0.49340154, 0.36172116, 0.41739266],
              [0.27505083, 0.34639281, 0.14758779],
              [0.50307347, 0.41092623, 0.08538175]],
      
             [[0.6697906 , 0.40899173, 0.73265156],
              [0.63231443, 0.40987279, 0.8585983 ],
              [0.33083785, 0.45004791, 0.92705803],
              ...,
              [0.48935691, 0.49467794, 1.01295998],
              [0.44510797, 0.52991035, 1.08132399],
              [0.47965262, 0.45470307, 1.13437158]],
      
             [[0.34954657, 0.30423   , 0.33940372],
              [0.3663739 , 0.28138215, 0.46673025],
              [0.3639808 , 0.35480344, 0.50010027],
              ...,
              [0.63094498, 0.33266783, 0.62103783],
              [0.65253291, 0.35838869, 0.6875826 ],
              [0.55743991, 0.2230277 , 0.52674879]],
      
             [[0.45621561, 0.4814433 , 0.15078173],
              [0.75799236, 0.50949934, 0.4323404 ],
              [0.73309182, 0.73403857, 0.23684961],
              ...,
              [0.35197736, 0.39981316, 0.68034878],
              [0.33940493, 0.3816481 , 0.50998822],
              [0.49475088, 0.50196129, 0.32731979]]])

    • omega_United Kingdom
      (chain, draw, omega_United Kingdom_dim_0, omega_United Kingdom_dim_1)
      float64
      0.02544 0.0 ... -0.01106 0.02829

      array([[[[ 0.02543666,  0.        ,  0.        ],
               [ 0.02006354,  0.01133659,  0.        ],
               [ 0.04131264, -0.00256865,  0.02887998]],
      
              [[ 0.02549925,  0.        ,  0.        ],
               [ 0.0185183 ,  0.00946872,  0.        ],
               [ 0.043243  , -0.00733574,  0.03162954]],
      
              [[ 0.0239479 ,  0.        ,  0.        ],
               [ 0.01654327,  0.01014025,  0.        ],
               [ 0.03652538, -0.00297742,  0.02638851]],
      
              ...,
      
              [[ 0.02832849,  0.        ,  0.        ],
               [ 0.01965147,  0.01036701,  0.        ],
               [ 0.04235752, -0.00157911,  0.03311147]],
      
              [[ 0.02435381,  0.        ,  0.        ],
               [ 0.0177562 ,  0.01068459,  0.        ],
      ...
               [ 0.02055434,  0.01081319,  0.        ],
               [ 0.04488657, -0.0039854 ,  0.03301123]],
      
              [[ 0.02719916,  0.        ,  0.        ],
               [ 0.01848579,  0.01219467,  0.        ],
               [ 0.04251097, -0.00132384,  0.02652562]],
      
              ...,
      
              [[ 0.02471302,  0.        ,  0.        ],
               [ 0.01817112,  0.01119504,  0.        ],
               [ 0.04095206, -0.00400516,  0.03402911]],
      
              [[ 0.02572545,  0.        ,  0.        ],
               [ 0.01783698,  0.01087901,  0.        ],
               [ 0.04135835, -0.0064794 ,  0.03091845]],
      
              [[ 0.02875208,  0.        ,  0.        ],
               [ 0.02196562,  0.01197236,  0.        ],
               [ 0.04070217, -0.01106366,  0.02829107]]]])

    • betaX_United States
      (chain, draw, betaX_United States_dim_0, betaX_United States_dim_1)
      float64
      0.009227 0.003603 ... 0.009821

      array([[[[ 9.22722045e-03,  3.60275979e-03,  1.03413214e-03],
               [-3.34614989e-04, -4.28796096e-03, -1.35563330e-02],
               [ 5.11764460e-04,  6.43801265e-03,  7.73929452e-03],
               ...,
               [ 5.76870749e-03,  6.27007420e-03,  8.23227802e-03],
               [ 7.38431288e-03,  8.69752703e-03,  1.00594222e-02],
               [ 7.96822737e-03,  7.90918043e-03,  8.92412008e-03]],
      
              [[ 5.09639332e-03,  8.26151542e-03,  3.80693518e-04],
               [ 2.42408780e-03,  1.42977368e-03, -1.72811375e-03],
               [-9.40735942e-04, -3.31338691e-03,  1.03571680e-02],
               ...,
               [ 6.83335339e-04,  2.23986284e-03,  5.60782260e-03],
               [ 9.64568428e-04,  2.62831868e-03,  6.90049169e-03],
               [ 1.70169434e-03,  3.80864674e-03,  5.99356634e-03]],
      
              [[ 8.69689260e-03,  7.00224941e-03,  9.86526589e-06],
               [ 2.31349350e-03,  1.78440350e-03, -3.00448101e-03],
               [-2.42490086e-03, -1.88417718e-03,  1.32421872e-02],
               ...,
      ...
               ...,
               [ 2.61912113e-03,  1.64929777e-03,  9.36155922e-03],
               [ 2.74610370e-03,  2.23750225e-03,  1.07090483e-02],
               [ 4.07038526e-03,  1.67622153e-03,  9.23124744e-03]],
      
              [[ 7.08269640e-03,  3.31030736e-04,  1.41251160e-03],
               [-1.13619758e-03, -3.66125307e-03, -3.95184935e-03],
               [-9.69577767e-04,  1.13394403e-03,  1.49765738e-02],
               ...,
               [ 2.80170646e-03,  2.35261424e-03,  8.50181539e-03],
               [ 2.97485313e-03,  3.36437811e-03,  9.72913924e-03],
               [ 3.99169638e-03,  2.90549668e-03,  8.80270684e-03]],
      
              [[ 5.76478736e-03, -5.12266740e-04,  4.32993535e-03],
               [-8.04535286e-04, -5.02750672e-03, -2.30536451e-03],
               [ 4.31438297e-03,  5.49012222e-03,  1.32219934e-02],
               ...,
               [ 4.21131517e-03,  4.35513754e-03,  8.79475388e-03],
               [ 4.40069853e-03,  4.85238612e-03,  1.03729712e-02],
               [ 4.98825667e-03,  4.26289486e-03,  9.82111912e-03]]]])

    • noise_chol_United States_corr
      (chain, draw, noise_chol_United States_corr_dim_0, noise_chol_United States_corr_dim_1)
      float64
      1.0 -0.1237 0.2194 ... -0.3669 1.0

      array([[[[ 1.        , -0.12373496,  0.2194029 ],
               [-0.12373496,  1.        , -0.25418072],
               [ 0.2194029 , -0.25418072,  1.        ]],
      
              [[ 1.        , -0.08755801,  0.16400819],
               [-0.08755801,  1.        , -0.09966876],
               [ 0.16400819, -0.09966876,  1.        ]],
      
              [[ 1.        ,  0.10421435,  0.31071612],
               [ 0.10421435,  1.        , -0.07786102],
               [ 0.31071612, -0.07786102,  1.        ]],
      
              ...,
      
              [[ 1.        , -0.25690227, -0.2516993 ],
               [-0.25690227,  1.        , -0.16348354],
               [-0.2516993 , -0.16348354,  1.        ]],
      
              [[ 1.        ,  0.13805707,  0.1129058 ],
               [ 0.13805707,  1.        ,  0.03887161],
      ...
               [-0.24519414,  1.        ,  0.18560319],
               [-0.04654987,  0.18560319,  1.        ]],
      
              [[ 1.        , -0.08347974,  0.08345532],
               [-0.08347974,  1.        , -0.16184667],
               [ 0.08345532, -0.16184667,  1.        ]],
      
              ...,
      
              [[ 1.        ,  0.09031447,  0.01845146],
               [ 0.09031447,  1.        ,  0.07953875],
               [ 0.01845146,  0.07953875,  1.        ]],
      
              [[ 1.        , -0.08492667, -0.06105887],
               [-0.08492667,  1.        , -0.09564229],
               [-0.06105887, -0.09564229,  1.        ]],
      
              [[ 1.        , -0.07369983,  0.19028836],
               [-0.07369983,  1.        , -0.36687185],
               [ 0.19028836, -0.36687185,  1.        ]]]])

    • noise_chol_United States_stds
      (chain, draw, noise_chol_United States_stds_dim_0)
      float64
      0.3961 0.1731 ... 0.236 0.04284

      array([[[0.39610121, 0.17313566, 0.13151658],
              [0.50300257, 0.16378312, 0.30785359],
              [0.40499367, 0.29183097, 0.17103799],
              ...,
              [0.25308695, 0.225279  , 0.0499346 ],
              [0.18360867, 0.14793039, 0.10335308],
              [0.13763278, 0.27036949, 0.25001474]],
      
             [[0.33901425, 0.2859728 , 0.14938787],
              [0.46199928, 0.24372264, 0.38710875],
              [0.18262759, 0.20826379, 0.15278749],
              ...,
              [0.22499492, 0.26278119, 0.64153824],
              [0.28685874, 0.27750089, 0.57339015],
              [0.22616996, 0.26611302, 0.81114613]],
      
             [[0.26858195, 0.26946796, 0.01240314],
              [0.19922095, 0.23897807, 0.03079663],
              [0.23627217, 0.25924429, 0.06318893],
              ...,
              [0.47553886, 0.16034714, 0.5655458 ],
              [0.47969097, 0.15234592, 0.45064874],
              [0.5480807 , 0.12355644, 0.19380373]],
      
             [[0.35877391, 0.24909448, 0.08051716],
              [0.53630726, 0.29214595, 0.0914405 ],
              [0.45646339, 0.49269993, 0.1171669 ],
              ...,
              [0.24895896, 0.30515014, 0.05616936],
              [0.17878626, 0.23102656, 0.03243802],
              [0.23670972, 0.23603791, 0.04284113]]])

    • omega_United States
      (chain, draw, omega_United States_dim_0, omega_United States_dim_1)
      float64
      0.02224 0.0 ... -0.007916 0.02205

      array([[[[ 0.02224269,  0.        ,  0.        ],
               [ 0.01426655,  0.00781906,  0.        ],
               [ 0.04297316, -0.0029042 ,  0.02139896]],
      
              [[ 0.02161116,  0.        ,  0.        ],
               [ 0.01442107,  0.00699402,  0.        ],
               [ 0.04733589, -0.00850155,  0.02438742]],
      
              [[ 0.02154883,  0.        ,  0.        ],
               [ 0.01541935,  0.00865652,  0.        ],
               [ 0.04205062, -0.00440743,  0.01687921]],
      
              ...,
      
              [[ 0.02182073,  0.        ,  0.        ],
               [ 0.0120993 ,  0.00850836,  0.        ],
               [ 0.04378857, -0.00264491,  0.02324224]],
      
              [[ 0.02189389,  0.        ,  0.        ],
               [ 0.01425134,  0.00623576,  0.        ],
      ...
               [ 0.01523062,  0.00780871,  0.        ],
               [ 0.04675563, -0.00378547,  0.02724154]],
      
              [[ 0.02275317,  0.        ,  0.        ],
               [ 0.01453993,  0.00875474,  0.        ],
               [ 0.04320462, -0.0011659 ,  0.02463757]],
      
              ...,
      
              [[ 0.02200213,  0.        ,  0.        ],
               [ 0.01366546,  0.01006372,  0.        ],
               [ 0.04291484, -0.0076015 ,  0.0180956 ]],
      
              [[ 0.02158716,  0.        ,  0.        ],
               [ 0.01363408,  0.0076984 ,  0.        ],
               [ 0.04297396, -0.00866316,  0.01888493]],
      
              [[ 0.02238792,  0.        ,  0.        ],
               [ 0.01314157,  0.00867913,  0.        ],
               [ 0.04180196, -0.00791556,  0.02205044]]]])

  • Indexes: (73)
    • chain
      PandasIndex

      PandasIndex(Int64Index([0, 1, 2, 3], dtype='int64', name='chain'))

    • draw
      PandasIndex

      PandasIndex(Int64Index([   0,    1,    2,    3,    4,    5,    6,    7,    8,    9,
                  ...
                  1990, 1991, 1992, 1993, 1994, 1995, 1996, 1997, 1998, 1999],
                 dtype='int64', name='draw', length=2000))

    • equations
      PandasIndex

      PandasIndex(Index(['dl_gdp', 'dl_cons', 'dl_gfcf'], dtype='object', name='equations'))

    • lags
      PandasIndex

      PandasIndex(Int64Index([1, 2], dtype='int64', name='lags'))

    • cross_vars
      PandasIndex

      PandasIndex(Index(['dl_gdp', 'dl_cons', 'dl_gfcf'], dtype='object', name='cross_vars'))

    • omega_global_dim_0
      PandasIndex

      PandasIndex(Int64Index([0, 1, 2, 3, 4, 5], dtype='int64', name='omega_global_dim_0'))

    • noise_chol_Australia_dim_0
      PandasIndex

      PandasIndex(Int64Index([0, 1, 2, 3, 4, 5], dtype='int64', name='noise_chol_Australia_dim_0'))

    • noise_chol_Canada_dim_0
      PandasIndex

      PandasIndex(Int64Index([0, 1, 2, 3, 4, 5], dtype='int64', name='noise_chol_Canada_dim_0'))

    • noise_chol_Chile_dim_0
      PandasIndex

      PandasIndex(Int64Index([0, 1, 2, 3, 4, 5], dtype='int64', name='noise_chol_Chile_dim_0'))

    • noise_chol_Ireland_dim_0
      PandasIndex

      PandasIndex(Int64Index([0, 1, 2, 3, 4, 5], dtype='int64', name='noise_chol_Ireland_dim_0'))

    • noise_chol_New Zealand_dim_0
      PandasIndex

      PandasIndex(Int64Index([0, 1, 2, 3, 4, 5], dtype='int64', name='noise_chol_New Zealand_dim_0'))

    • noise_chol_South Africa_dim_0
      PandasIndex

      PandasIndex(Int64Index([0, 1, 2, 3, 4, 5], dtype='int64', name='noise_chol_South Africa_dim_0'))

    • noise_chol_United Kingdom_dim_0
      PandasIndex

      PandasIndex(Int64Index([0, 1, 2, 3, 4, 5], dtype='int64', name='noise_chol_United Kingdom_dim_0'))

    • noise_chol_United States_dim_0
      PandasIndex

      PandasIndex(Int64Index([0, 1, 2, 3, 4, 5], dtype='int64', name='noise_chol_United States_dim_0'))

    • omega_global_corr_dim_0
      PandasIndex

      PandasIndex(Int64Index([0, 1, 2], dtype='int64', name='omega_global_corr_dim_0'))

    • omega_global_corr_dim_1
      PandasIndex

      PandasIndex(Int64Index([0, 1, 2], dtype='int64', name='omega_global_corr_dim_1'))

    • omega_global_stds_dim_0
      PandasIndex

      PandasIndex(Int64Index([0, 1, 2], dtype='int64', name='omega_global_stds_dim_0'))

    • betaX_Australia_dim_0
      PandasIndex

      PandasIndex(Int64Index([ 0,  1,  2,  3,  4,  5,  6,  7,  8,  9, 10, 11, 12, 13, 14, 15, 16,
                  17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33,
                  34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48],
                 dtype='int64', name='betaX_Australia_dim_0'))

    • betaX_Australia_dim_1
      PandasIndex

      PandasIndex(Int64Index([0, 1, 2], dtype='int64', name='betaX_Australia_dim_1'))

    • noise_chol_Australia_corr_dim_0
      PandasIndex

      PandasIndex(Int64Index([0, 1, 2], dtype='int64', name='noise_chol_Australia_corr_dim_0'))

    • noise_chol_Australia_corr_dim_1
      PandasIndex

      PandasIndex(Int64Index([0, 1, 2], dtype='int64', name='noise_chol_Australia_corr_dim_1'))

    • noise_chol_Australia_stds_dim_0
      PandasIndex

      PandasIndex(Int64Index([0, 1, 2], dtype='int64', name='noise_chol_Australia_stds_dim_0'))

    • omega_Australia_dim_0
      PandasIndex

      PandasIndex(Int64Index([0, 1, 2], dtype='int64', name='omega_Australia_dim_0'))

    • omega_Australia_dim_1
      PandasIndex

      PandasIndex(Int64Index([0, 1, 2], dtype='int64', name='omega_Australia_dim_1'))

    • betaX_Canada_dim_0
      PandasIndex

      PandasIndex(Int64Index([0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18,
                  19, 20, 21],
                 dtype='int64', name='betaX_Canada_dim_0'))

    • betaX_Canada_dim_1
      PandasIndex

      PandasIndex(Int64Index([0, 1, 2], dtype='int64', name='betaX_Canada_dim_1'))

    • noise_chol_Canada_corr_dim_0
      PandasIndex

      PandasIndex(Int64Index([0, 1, 2], dtype='int64', name='noise_chol_Canada_corr_dim_0'))

    • noise_chol_Canada_corr_dim_1
      PandasIndex

      PandasIndex(Int64Index([0, 1, 2], dtype='int64', name='noise_chol_Canada_corr_dim_1'))

    • noise_chol_Canada_stds_dim_0
      PandasIndex

      PandasIndex(Int64Index([0, 1, 2], dtype='int64', name='noise_chol_Canada_stds_dim_0'))

    • omega_Canada_dim_0
      PandasIndex

      PandasIndex(Int64Index([0, 1, 2], dtype='int64', name='omega_Canada_dim_0'))

    • omega_Canada_dim_1
      PandasIndex

      PandasIndex(Int64Index([0, 1, 2], dtype='int64', name='omega_Canada_dim_1'))

    • betaX_Chile_dim_0
      PandasIndex

      PandasIndex(Int64Index([ 0,  1,  2,  3,  4,  5,  6,  7,  8,  9, 10, 11, 12, 13, 14, 15, 16,
                  17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33,
                  34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48],
                 dtype='int64', name='betaX_Chile_dim_0'))

    • betaX_Chile_dim_1
      PandasIndex

      PandasIndex(Int64Index([0, 1, 2], dtype='int64', name='betaX_Chile_dim_1'))

    • noise_chol_Chile_corr_dim_0
      PandasIndex

      PandasIndex(Int64Index([0, 1, 2], dtype='int64', name='noise_chol_Chile_corr_dim_0'))

    • noise_chol_Chile_corr_dim_1
      PandasIndex

      PandasIndex(Int64Index([0, 1, 2], dtype='int64', name='noise_chol_Chile_corr_dim_1'))

    • noise_chol_Chile_stds_dim_0
      PandasIndex

      PandasIndex(Int64Index([0, 1, 2], dtype='int64', name='noise_chol_Chile_stds_dim_0'))

    • omega_Chile_dim_0
      PandasIndex

      PandasIndex(Int64Index([0, 1, 2], dtype='int64', name='omega_Chile_dim_0'))

    • omega_Chile_dim_1
      PandasIndex

      PandasIndex(Int64Index([0, 1, 2], dtype='int64', name='omega_Chile_dim_1'))

    • betaX_Ireland_dim_0
      PandasIndex

      PandasIndex(Int64Index([ 0,  1,  2,  3,  4,  5,  6,  7,  8,  9, 10, 11, 12, 13, 14, 15, 16,
                  17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33,
                  34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48],
                 dtype='int64', name='betaX_Ireland_dim_0'))

    • betaX_Ireland_dim_1
      PandasIndex

      PandasIndex(Int64Index([0, 1, 2], dtype='int64', name='betaX_Ireland_dim_1'))

    • noise_chol_Ireland_corr_dim_0
      PandasIndex

      PandasIndex(Int64Index([0, 1, 2], dtype='int64', name='noise_chol_Ireland_corr_dim_0'))

    • noise_chol_Ireland_corr_dim_1
      PandasIndex

      PandasIndex(Int64Index([0, 1, 2], dtype='int64', name='noise_chol_Ireland_corr_dim_1'))

    • noise_chol_Ireland_stds_dim_0
      PandasIndex

      PandasIndex(Int64Index([0, 1, 2], dtype='int64', name='noise_chol_Ireland_stds_dim_0'))

    • omega_Ireland_dim_0
      PandasIndex

      PandasIndex(Int64Index([0, 1, 2], dtype='int64', name='omega_Ireland_dim_0'))

    • omega_Ireland_dim_1
      PandasIndex

      PandasIndex(Int64Index([0, 1, 2], dtype='int64', name='omega_Ireland_dim_1'))

    • betaX_New Zealand_dim_0
      PandasIndex

      PandasIndex(Int64Index([ 0,  1,  2,  3,  4,  5,  6,  7,  8,  9, 10, 11, 12, 13, 14, 15, 16,
                  17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33,
                  34, 35, 36, 37, 38, 39, 40],
                 dtype='int64', name='betaX_New Zealand_dim_0'))

    • betaX_New Zealand_dim_1
      PandasIndex

      PandasIndex(Int64Index([0, 1, 2], dtype='int64', name='betaX_New Zealand_dim_1'))

    • noise_chol_New Zealand_corr_dim_0
      PandasIndex

      PandasIndex(Int64Index([0, 1, 2], dtype='int64', name='noise_chol_New Zealand_corr_dim_0'))

    • noise_chol_New Zealand_corr_dim_1
      PandasIndex

      PandasIndex(Int64Index([0, 1, 2], dtype='int64', name='noise_chol_New Zealand_corr_dim_1'))

    • noise_chol_New Zealand_stds_dim_0
      PandasIndex

      PandasIndex(Int64Index([0, 1, 2], dtype='int64', name='noise_chol_New Zealand_stds_dim_0'))

    • omega_New Zealand_dim_0
      PandasIndex

      PandasIndex(Int64Index([0, 1, 2], dtype='int64', name='omega_New Zealand_dim_0'))

    • omega_New Zealand_dim_1
      PandasIndex

      PandasIndex(Int64Index([0, 1, 2], dtype='int64', name='omega_New Zealand_dim_1'))

    • betaX_South Africa_dim_0
      PandasIndex

      PandasIndex(Int64Index([ 0,  1,  2,  3,  4,  5,  6,  7,  8,  9, 10, 11, 12, 13, 14, 15, 16,
                  17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33,
                  34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48],
                 dtype='int64', name='betaX_South Africa_dim_0'))

    • betaX_South Africa_dim_1
      PandasIndex

      PandasIndex(Int64Index([0, 1, 2], dtype='int64', name='betaX_South Africa_dim_1'))

    • noise_chol_South Africa_corr_dim_0
      PandasIndex

      PandasIndex(Int64Index([0, 1, 2], dtype='int64', name='noise_chol_South Africa_corr_dim_0'))

    • noise_chol_South Africa_corr_dim_1
      PandasIndex

      PandasIndex(Int64Index([0, 1, 2], dtype='int64', name='noise_chol_South Africa_corr_dim_1'))

    • noise_chol_South Africa_stds_dim_0
      PandasIndex

      PandasIndex(Int64Index([0, 1, 2], dtype='int64', name='noise_chol_South Africa_stds_dim_0'))

    • omega_South Africa_dim_0
      PandasIndex

      PandasIndex(Int64Index([0, 1, 2], dtype='int64', name='omega_South Africa_dim_0'))

    • omega_South Africa_dim_1
      PandasIndex

      PandasIndex(Int64Index([0, 1, 2], dtype='int64', name='omega_South Africa_dim_1'))

    • betaX_United Kingdom_dim_0
      PandasIndex

      PandasIndex(Int64Index([ 0,  1,  2,  3,  4,  5,  6,  7,  8,  9, 10, 11, 12, 13, 14, 15, 16,
                  17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33,
                  34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48],
                 dtype='int64', name='betaX_United Kingdom_dim_0'))

    • betaX_United Kingdom_dim_1
      PandasIndex

      PandasIndex(Int64Index([0, 1, 2], dtype='int64', name='betaX_United Kingdom_dim_1'))

    • noise_chol_United Kingdom_corr_dim_0
      PandasIndex

      PandasIndex(Int64Index([0, 1, 2], dtype='int64', name='noise_chol_United Kingdom_corr_dim_0'))

    • noise_chol_United Kingdom_corr_dim_1
      PandasIndex

      PandasIndex(Int64Index([0, 1, 2], dtype='int64', name='noise_chol_United Kingdom_corr_dim_1'))

    • noise_chol_United Kingdom_stds_dim_0
      PandasIndex

      PandasIndex(Int64Index([0, 1, 2], dtype='int64', name='noise_chol_United Kingdom_stds_dim_0'))

    • omega_United Kingdom_dim_0
      PandasIndex

      PandasIndex(Int64Index([0, 1, 2], dtype='int64', name='omega_United Kingdom_dim_0'))

    • omega_United Kingdom_dim_1
      PandasIndex

      PandasIndex(Int64Index([0, 1, 2], dtype='int64', name='omega_United Kingdom_dim_1'))

    • betaX_United States_dim_0
      PandasIndex

      PandasIndex(Int64Index([ 0,  1,  2,  3,  4,  5,  6,  7,  8,  9, 10, 11, 12, 13, 14, 15, 16,
                  17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33,
                  34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45],
                 dtype='int64', name='betaX_United States_dim_0'))

    • betaX_United States_dim_1
      PandasIndex

      PandasIndex(Int64Index([0, 1, 2], dtype='int64', name='betaX_United States_dim_1'))

    • noise_chol_United States_corr_dim_0
      PandasIndex

      PandasIndex(Int64Index([0, 1, 2], dtype='int64', name='noise_chol_United States_corr_dim_0'))

    • noise_chol_United States_corr_dim_1
      PandasIndex

      PandasIndex(Int64Index([0, 1, 2], dtype='int64', name='noise_chol_United States_corr_dim_1'))

    • noise_chol_United States_stds_dim_0
      PandasIndex

      PandasIndex(Int64Index([0, 1, 2], dtype='int64', name='noise_chol_United States_stds_dim_0'))

    • omega_United States_dim_0
      PandasIndex

      PandasIndex(Int64Index([0, 1, 2], dtype='int64', name='omega_United States_dim_0'))

    • omega_United States_dim_1
      PandasIndex

      PandasIndex(Int64Index([0, 1, 2], dtype='int64', name='omega_United States_dim_1'))

  • Attributes: (2)

    created_at :

    2023-02-21T19:24:14.259388

    arviz_version :

    0.14.0

  
  
• posterior_predictive

  <xarray.Dataset>
  Dimensions:                   (chain: 4, draw: 2000, obs_Australia_dim_2: 49,
                                 obs_Australia_dim_3: 3, obs_Canada_dim_2: 22,
                                 obs_Canada_dim_3: 3, obs_Chile_dim_2: 49,
                                 obs_Chile_dim_3: 3, obs_Ireland_dim_2: 49,
                                 obs_Ireland_dim_3: 3, obs_New Zealand_dim_2: 41,
                                 obs_New Zealand_dim_3: 3,
                                 obs_South Africa_dim_2: 49,
                                 obs_South Africa_dim_3: 3,
                                 obs_United Kingdom_dim_2: 49,
                                 obs_United Kingdom_dim_3: 3,
                                 obs_United States_dim_2: 46,
                                 obs_United States_dim_3: 3)
  Coordinates: (12/18)
    * chain                     (chain) int64 0 1 2 3
    * draw                      (draw) int64 0 1 2 3 4 ... 1996 1997 1998 1999
    * obs_Australia_dim_2       (obs_Australia_dim_2) int64 0 1 2 3 ... 46 47 48
    * obs_Australia_dim_3       (obs_Australia_dim_3) int64 0 1 2
    * obs_Canada_dim_2          (obs_Canada_dim_2) int64 0 1 2 3 4 ... 18 19 20 21
    * obs_Canada_dim_3          (obs_Canada_dim_3) int64 0 1 2
      ...                        ...
    * obs_South Africa_dim_2    (obs_South Africa_dim_2) int64 0 1 2 ... 46 47 48
    * obs_South Africa_dim_3    (obs_South Africa_dim_3) int64 0 1 2
    * obs_United Kingdom_dim_2  (obs_United Kingdom_dim_2) int64 0 1 2 ... 47 48
    * obs_United Kingdom_dim_3  (obs_United Kingdom_dim_3) int64 0 1 2
    * obs_United States_dim_2   (obs_United States_dim_2) int64 0 1 2 ... 43 44 45
    * obs_United States_dim_3   (obs_United States_dim_3) int64 0 1 2
  Data variables:
      obs_Australia             (chain, draw, obs_Australia_dim_2, obs_Australia_dim_3) float64 ...
      obs_Canada                (chain, draw, obs_Canada_dim_2, obs_Canada_dim_3) float64 ...
      obs_Chile                 (chain, draw, obs_Chile_dim_2, obs_Chile_dim_3) float64 ...
      obs_Ireland               (chain, draw, obs_Ireland_dim_2, obs_Ireland_dim_3) float64 ...
      obs_New Zealand           (chain, draw, obs_New Zealand_dim_2, obs_New Zealand_dim_3) float64 ...
      obs_South Africa          (chain, draw, obs_South Africa_dim_2, obs_South Africa_dim_3) float64 ...
      obs_United Kingdom        (chain, draw, obs_United Kingdom_dim_2, obs_United Kingdom_dim_3) float64 ...
      obs_United States         (chain, draw, obs_United States_dim_2, obs_United States_dim_3) float64 ...
  Attributes:
      created_at:                 2023-02-21T19:31:34.868405
      arviz_version:              0.14.0
      inference_library:          pymc
      inference_library_version:  5.0.1

  xarray.Dataset

  • Dimensions:
    • chain: 4
    • draw: 2000
    • obs_Australia_dim_2: 49
    • obs_Australia_dim_3: 3
    • obs_Canada_dim_2: 22
    • obs_Canada_dim_3: 3
    • obs_Chile_dim_2: 49
    • obs_Chile_dim_3: 3
    • obs_Ireland_dim_2: 49
    • obs_Ireland_dim_3: 3
    • obs_New Zealand_dim_2: 41
    • obs_New Zealand_dim_3: 3
    • obs_South Africa_dim_2: 49
    • obs_South Africa_dim_3: 3
    • obs_United Kingdom_dim_2: 49
    • obs_United Kingdom_dim_3: 3
    • obs_United States_dim_2: 46
    • obs_United States_dim_3: 3
  • Coordinates: (18)
    • chain
      (chain)
      int64
      0 1 2 3

      array([0, 1, 2, 3])

    • draw
      (draw)
      int64
      0 1 2 3 4 ... 1996 1997 1998 1999

      array([   0,    1,    2, ..., 1997, 1998, 1999])

    • obs_Australia_dim_2
      (obs_Australia_dim_2)
      int64
      0 1 2 3 4 5 6 ... 43 44 45 46 47 48

      array([ 0,  1,  2,  3,  4,  5,  6,  7,  8,  9, 10, 11, 12, 13, 14, 15, 16, 17,
             18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35,
             36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48])

    • obs_Australia_dim_3
      (obs_Australia_dim_3)
      int64
      0 1 2

      array([0, 1, 2])

    • obs_Canada_dim_2
      (obs_Canada_dim_2)
      int64
      0 1 2 3 4 5 6 ... 16 17 18 19 20 21

      array([ 0,  1,  2,  3,  4,  5,  6,  7,  8,  9, 10, 11, 12, 13, 14, 15, 16, 17,
             18, 19, 20, 21])

    • obs_Canada_dim_3
      (obs_Canada_dim_3)
      int64
      0 1 2

      array([0, 1, 2])

    • obs_Chile_dim_2
      (obs_Chile_dim_2)
      int64
      0 1 2 3 4 5 6 ... 43 44 45 46 47 48

      array([ 0,  1,  2,  3,  4,  5,  6,  7,  8,  9, 10, 11, 12, 13, 14, 15, 16, 17,
             18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35,
             36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48])

    • obs_Chile_dim_3
      (obs_Chile_dim_3)
      int64
      0 1 2

      array([0, 1, 2])

    • obs_Ireland_dim_2
      (obs_Ireland_dim_2)
      int64
      0 1 2 3 4 5 6 ... 43 44 45 46 47 48

      array([ 0,  1,  2,  3,  4,  5,  6,  7,  8,  9, 10, 11, 12, 13, 14, 15, 16, 17,
             18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35,
             36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48])

    • obs_Ireland_dim_3
      (obs_Ireland_dim_3)
      int64
      0 1 2

      array([0, 1, 2])

    • obs_New Zealand_dim_2
      (obs_New Zealand_dim_2)
      int64
      0 1 2 3 4 5 6 ... 35 36 37 38 39 40

      array([ 0,  1,  2,  3,  4,  5,  6,  7,  8,  9, 10, 11, 12, 13, 14, 15, 16, 17,
             18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35,
             36, 37, 38, 39, 40])

    • obs_New Zealand_dim_3
      (obs_New Zealand_dim_3)
      int64
      0 1 2

      array([0, 1, 2])

    • obs_South Africa_dim_2
      (obs_South Africa_dim_2)
      int64
      0 1 2 3 4 5 6 ... 43 44 45 46 47 48

      array([ 0,  1,  2,  3,  4,  5,  6,  7,  8,  9, 10, 11, 12, 13, 14, 15, 16, 17,
             18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35,
             36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48])

    • obs_South Africa_dim_3
      (obs_South Africa_dim_3)
      int64
      0 1 2

      array([0, 1, 2])

    • obs_United Kingdom_dim_2
      (obs_United Kingdom_dim_2)
      int64
      0 1 2 3 4 5 6 ... 43 44 45 46 47 48

      array([ 0,  1,  2,  3,  4,  5,  6,  7,  8,  9, 10, 11, 12, 13, 14, 15, 16, 17,
             18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35,
             36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48])

    • obs_United Kingdom_dim_3
      (obs_United Kingdom_dim_3)
      int64
      0 1 2

      array([0, 1, 2])

    • obs_United States_dim_2
      (obs_United States_dim_2)
      int64
      0 1 2 3 4 5 6 ... 40 41 42 43 44 45

      array([ 0,  1,  2,  3,  4,  5,  6,  7,  8,  9, 10, 11, 12, 13, 14, 15, 16, 17,
             18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35,
             36, 37, 38, 39, 40, 41, 42, 43, 44, 45])

    • obs_United States_dim_3
      (obs_United States_dim_3)
      int64
      0 1 2

      array([0, 1, 2])

  • Data variables: (8)
    • obs_Australia
      (chain, draw, obs_Australia_dim_2, obs_Australia_dim_3)
      float64
      0.01718 0.03863 ... 0.01568 0.02849

      array([[[[ 1.71814304e-02,  3.86304132e-02,  8.62497633e-03],
               [ 3.72827017e-02,  2.32908100e-02,  4.65201150e-02],
               [ 1.56932521e-02,  1.75517726e-02,  4.09380858e-02],
               ...,
               [ 4.10301093e-02,  4.62873493e-02,  1.15345906e-01],
               [ 3.95068453e-03,  1.66705131e-02, -1.22055946e-02],
               [ 1.61741262e-02,  2.00958780e-02,  4.75676040e-02]],
      
              [[ 1.16765646e-02,  4.34190246e-02,  1.17997888e-02],
               [ 3.70198818e-02,  4.49392262e-02,  6.63994229e-02],
               [ 2.29244731e-03,  3.70708820e-02, -8.81318993e-02],
               ...,
               [ 4.06237200e-02,  3.38910413e-02,  5.24163359e-02],
               [ 2.45360155e-02,  3.27939557e-02,  9.95139123e-02],
               [ 1.18874430e-02,  1.24712580e-03, -3.16569114e-02]],
      
              [[ 3.78454998e-02,  5.97333817e-02,  6.57289700e-02],
               [ 3.42922279e-02,  1.98606073e-02,  5.86488810e-02],
               [ 2.97512375e-02,  5.08368977e-02,  1.44429184e-02],
               ...,
      ...
               ...,
               [-7.82775100e-03, -1.11524239e-02,  1.33931778e-02],
               [ 1.04920189e-02,  2.95794905e-02, -4.20372757e-02],
               [ 1.25868172e-02,  8.26226518e-03,  2.32814476e-02]],
      
              [[ 4.22496563e-02,  3.93804556e-02,  6.17123928e-02],
               [ 5.75016873e-02,  2.83514497e-02,  1.29165220e-01],
               [ 9.63236659e-03,  2.90319014e-02,  3.65130736e-02],
               ...,
               [ 2.54372236e-02,  1.22418583e-02,  3.11397189e-02],
               [ 3.37716207e-02,  2.88003128e-02,  6.13473952e-02],
               [ 4.59080412e-02,  4.35640830e-02,  1.02486032e-01]],
      
              [[ 2.69865820e-02,  2.75567929e-02,  5.12639080e-02],
               [ 1.63093433e-02,  2.40403089e-02,  1.11878254e-02],
               [ 3.20637964e-02,  3.06880118e-02,  3.32248612e-02],
               ...,
               [ 1.52853345e-02,  2.57307871e-02, -1.14341035e-02],
               [ 1.15251256e-02,  3.50691462e-02, -5.55453149e-02],
               [ 1.15289667e-02,  1.56763222e-02,  2.84865123e-02]]]])

    • obs_Canada
      (chain, draw, obs_Canada_dim_2, obs_Canada_dim_3)
      float64
      -0.004644 0.000541 ... 0.01186

      array([[[[-4.64408169e-03,  5.41022474e-04,  2.77090992e-02],
               [ 7.65108310e-02,  4.20272316e-02,  4.29074280e-02],
               [ 7.63487440e-02,  5.93399341e-02,  2.21993532e-02],
               ...,
               [-4.88784351e-03,  1.89402137e-02,  5.13358215e-02],
               [ 3.09359293e-02,  2.63088702e-02,  3.34784431e-02],
               [-1.62071430e-02,  2.95699755e-03, -1.96588288e-02]],
      
              [[ 1.69427739e-02,  3.14504425e-02, -2.45921194e-02],
               [ 4.78292980e-02,  4.17053081e-02,  1.16101106e-01],
               [ 2.21984842e-02,  1.30568362e-02,  2.49782856e-02],
               ...,
               [-1.36514051e-02,  2.28260141e-02, -4.90129985e-02],
               [ 4.23434785e-02,  1.39910394e-02, -9.14378186e-03],
               [ 1.41931876e-03,  2.56539088e-03, -2.01969582e-02]],
      
              [[ 9.35860132e-03,  2.05013115e-02, -7.53635328e-02],
               [ 5.08839915e-02,  4.06375683e-02,  6.38489237e-02],
               [ 3.78814501e-02,  3.35364632e-02,  4.77189677e-02],
               ...,
      ...
               ...,
               [-2.43404641e-02,  1.05330236e-02, -7.31521306e-02],
               [-7.40980621e-03, -8.55092575e-03,  1.99562626e-02],
               [ 8.46992483e-03,  1.95258363e-02, -3.71379069e-04]],
      
              [[-3.32481115e-02, -5.09555042e-03, -6.69249055e-02],
               [ 2.86525876e-02,  2.61265843e-02,  7.45085394e-02],
               [ 2.94601432e-02,  3.67928245e-02,  6.20563008e-02],
               ...,
               [-2.53938240e-04,  1.58998304e-02, -1.97567736e-02],
               [-3.30727502e-02, -1.95918626e-02, -2.19663825e-02],
               [ 3.07192812e-02,  1.44959030e-02,  6.38936482e-03]],
      
              [[-5.55669235e-03,  1.34096637e-02, -2.80229050e-03],
               [ 4.48636450e-02,  4.32087685e-02,  1.64682437e-02],
               [ 4.45741963e-02,  5.19414321e-02, -7.16768194e-02],
               ...,
               [ 7.20579040e-04,  1.90249533e-02,  4.08664008e-02],
               [-3.45389840e-03,  9.57581651e-03,  1.34331022e-02],
               [ 1.33797090e-02,  4.79016262e-02,  1.18614703e-02]]]])

    • obs_Chile
      (chain, draw, obs_Chile_dim_2, obs_Chile_dim_3)
      float64
      0.06127 0.03212 ... 0.08228

      array([[[[ 6.12721183e-02,  3.21234017e-02, -4.03472510e-03],
               [ 9.81831038e-02,  7.56367935e-02,  3.00220526e-01],
               [-3.68627357e-02, -2.69241465e-02,  8.85175587e-02],
               ...,
               [ 6.65175085e-02, -3.07421617e-02,  1.67618155e-01],
               [ 7.17788445e-02,  9.60941741e-02,  1.12337786e-02],
               [ 4.37529878e-02,  4.24993573e-03,  1.38548876e-01]],
      
              [[ 8.62422526e-02,  7.59547740e-02,  2.11013291e-01],
               [-4.18916708e-02,  2.26006525e-02, -4.03739272e-02],
               [ 4.36567379e-02,  2.03844443e-02,  1.25405233e-01],
               ...,
               [ 2.46903978e-02,  3.19814849e-02,  9.10853274e-02],
               [-6.69388915e-02, -4.47635493e-02, -1.14852887e-01],
               [-1.12864431e-02, -8.30831365e-02,  3.79573314e-02]],
      
              [[ 8.11728592e-02,  3.46064296e-02,  1.38006803e-01],
               [ 8.66492371e-02,  1.54124190e-01,  9.23997087e-02],
               [ 8.72837690e-02,  8.65410217e-02,  9.36000724e-02],
               ...,
      ...
               ...,
               [ 5.79495015e-02,  1.32505013e-02,  6.20323360e-02],
               [ 3.59242864e-02,  8.75189010e-02,  1.26132245e-01],
               [ 1.51691936e-02,  3.39243983e-02,  1.85009169e-02]],
      
              [[-2.27000865e-02,  2.03228260e-03, -4.95550764e-02],
               [ 4.93748178e-02,  5.23312019e-02,  1.21542326e-01],
               [-1.79720053e-03, -5.77901061e-02,  4.97585606e-02],
               ...,
               [ 7.51790930e-02, -6.82322742e-03,  1.38309046e-01],
               [ 1.47121927e-02,  1.32441539e-02, -1.41932657e-01],
               [-6.58490525e-03, -2.03698972e-02, -5.22053183e-02]],
      
              [[ 8.65731987e-02,  8.21620479e-02,  5.84672407e-02],
               [-1.91285361e-02, -7.43787048e-02, -7.11719043e-02],
               [ 6.22570647e-02,  5.84276412e-02,  1.84151634e-01],
               ...,
               [ 3.89607458e-02,  2.18309257e-02,  1.11930753e-01],
               [ 1.28759433e-01,  7.40660544e-02,  3.00524095e-01],
               [ 1.78603328e-02,  7.96127549e-03,  8.22820066e-02]]]])

    • obs_Ireland
      (chain, draw, obs_Ireland_dim_2, obs_Ireland_dim_3)
      float64
      0.1557 0.08176 ... 0.1287 -0.1345

      array([[[[ 1.55690315e-01,  8.17612051e-02,  2.54884944e-01],
               [ 8.30537113e-02,  1.96665946e-02,  1.91948672e-01],
               [ 5.18063002e-02,  5.37948610e-02,  2.01020695e-02],
               ...,
               [-4.17005132e-02,  8.62801058e-03, -2.50714188e-02],
               [ 2.34376745e-02, -2.86949863e-02,  4.73413071e-02],
               [ 4.12567885e-02,  2.97175467e-02,  1.09204836e-02]],
      
              [[ 7.12140536e-02,  5.72404917e-02,  1.40261014e-01],
               [ 5.01194556e-02,  5.21749690e-02, -6.98677346e-02],
               [ 3.60390422e-03,  4.14117641e-02, -6.59201620e-02],
               ...,
               [ 8.32956157e-02,  4.80447074e-02,  2.77882427e-01],
               [ 3.15432944e-02, -5.43268717e-03,  2.16518669e-01],
               [ 7.67925538e-02,  9.95581466e-02,  3.24362526e-01]],
      
              [[ 1.02130912e-01,  7.24110686e-02,  2.33259953e-01],
               [ 8.76638592e-02,  2.77026372e-02, -1.28836810e-01],
               [ 3.81034380e-02,  2.48540029e-02, -2.91263272e-01],
               ...,
      ...
               ...,
               [ 4.69004828e-02,  7.92535331e-02,  1.62716290e-01],
               [ 4.44298900e-02, -2.36389271e-02,  3.84840773e-02],
               [ 6.47962921e-02,  7.12658913e-02,  1.09032776e-01]],
      
              [[ 1.45692181e-01,  9.76994510e-02,  1.16284048e-01],
               [ 9.98886023e-03,  2.38721537e-02,  1.37205085e-01],
               [ 1.13475116e-01,  9.52640604e-02,  5.53537026e-01],
               ...,
               [ 1.98637109e-03, -1.44739613e-02, -4.04618619e-03],
               [ 2.07201815e-02, -9.89853531e-03,  4.83800414e-02],
               [ 6.30169392e-02,  5.31426338e-02,  7.65845437e-02]],
      
              [[ 4.12936563e-03,  3.55472206e-02,  1.96776728e-01],
               [ 3.03932892e-02,  8.51055142e-03, -2.50454449e-01],
               [ 5.73927769e-02,  5.66884598e-02,  2.93782574e-01],
               ...,
               [-2.56240493e-02,  1.43019866e-02, -9.83973799e-02],
               [ 6.46347175e-02, -1.25078103e-02, -4.73941676e-02],
               [ 1.42690626e-01,  1.28735853e-01, -1.34536179e-01]]]])

    • obs_New Zealand
      (chain, draw, obs_New Zealand_dim_2, obs_New Zealand_dim_3)
      float64
      0.03207 0.02997 ... 0.03527 0.05695

      array([[[[ 3.20690633e-02,  2.99727795e-02,  6.17409380e-02],
               [-2.62744148e-02, -1.74185454e-02,  5.74588695e-02],
               [ 6.14617585e-03,  6.67343005e-03, -2.34943617e-02],
               ...,
               [ 3.01151769e-02,  3.01847683e-02,  7.40915874e-02],
               [ 4.60903541e-02,  4.94159825e-02,  8.83121067e-02],
               [ 4.52213957e-02,  3.48933527e-02,  1.19125066e-01]],
      
              [[ 4.02898888e-02,  2.22407120e-02,  7.61584903e-02],
               [ 2.87672463e-02,  2.62409068e-02, -1.34640321e-02],
               [ 4.44452188e-02,  5.58481770e-02,  8.33098440e-02],
               ...,
               [ 4.32440904e-02,  4.30665619e-02,  1.74801352e-01],
               [ 6.65765975e-03,  2.01150519e-03, -1.15729457e-02],
               [ 5.09384596e-02,  4.91561580e-02,  1.07038226e-01]],
      
              [[ 2.15312405e-02,  1.19202069e-02,  7.14022593e-02],
               [ 3.82029616e-02,  3.03344257e-02,  7.46014123e-02],
               [ 4.86917765e-02,  3.76701870e-02,  7.68651184e-02],
               ...,
      ...
               ...,
               [ 3.69542256e-02,  4.80030477e-03, -3.94413090e-02],
               [ 3.21254844e-02,  2.89474315e-02,  2.37307277e-02],
               [ 3.65098794e-02,  4.35925092e-02,  1.25754074e-01]],
      
              [[ 2.40271958e-02,  3.69412637e-02, -3.30688007e-02],
               [ 5.32477411e-02,  4.43699163e-02,  1.01855370e-01],
               [ 3.02279921e-02,  5.15357782e-02,  3.36666242e-02],
               ...,
               [ 2.32986286e-02,  2.17719747e-02,  4.38569710e-02],
               [ 9.90753293e-03,  2.49266878e-02, -1.53327898e-02],
               [ 1.61506414e-02,  3.21587798e-02, -5.85673173e-02]],
      
              [[ 2.53196637e-02,  4.13067995e-02,  6.94431362e-02],
               [ 5.02102734e-02,  2.53355885e-02,  1.97033240e-01],
               [ 3.47888163e-02,  4.30719282e-02,  6.21989311e-02],
               ...,
               [ 3.66163423e-02,  2.37704316e-02, -1.16997417e-02],
               [ 1.55158215e-02,  2.99695145e-02,  4.99092419e-02],
               [ 3.74461661e-02,  3.52667102e-02,  5.69489057e-02]]]])

    • obs_South Africa
      (chain, draw, obs_South Africa_dim_2, obs_South Africa_dim_3)
      float64
      0.03308 0.04329 ... -0.007726

      array([[[[ 3.30780556e-02,  4.32893911e-02,  6.05011744e-02],
               [-1.51739626e-04, -1.13314322e-02, -6.98970591e-02],
               [ 5.06024438e-02,  5.17561504e-02,  9.42083761e-02],
               ...,
               [ 5.54624849e-03, -3.15079810e-03, -1.47314096e-02],
               [ 2.08204734e-02,  2.75899818e-02, -1.83820743e-02],
               [-4.73507799e-03,  2.18914557e-02, -4.96872468e-02]],
      
              [[ 4.81253439e-02,  4.89427662e-02,  4.42420433e-02],
               [ 2.49053249e-02,  3.43137915e-02,  4.90914050e-02],
               [ 1.46720422e-02,  3.49305129e-02,  3.71172461e-02],
               ...,
               [-4.48067052e-03, -1.40509654e-02, -1.14008983e-01],
               [ 1.63492220e-02,  2.43939630e-02, -1.44261140e-02],
               [ 2.91068131e-02,  2.07542405e-02,  2.58933316e-02]],
      
              [[ 7.73081474e-02,  7.66319051e-02,  6.97183640e-02],
               [ 1.31293018e-02,  1.13030226e-02, -1.19635530e-01],
               [-2.73258731e-02, -6.94899442e-03, -4.09784834e-02],
               ...,
      ...
               ...,
               [ 5.04232684e-02,  5.28574979e-02,  1.24196528e-01],
               [ 1.63034069e-02,  2.85918028e-02,  4.63768417e-02],
               [ 2.28468022e-02,  8.97429649e-03,  1.21741339e-02]],
      
              [[ 1.21447075e-02, -2.23071080e-03,  2.54235225e-02],
               [ 2.48943153e-03, -3.75262990e-03, -2.55812651e-04],
               [ 3.38794359e-02,  1.90850623e-02,  7.09915282e-02],
               ...,
               [ 2.14291154e-02,  2.95327945e-02, -9.95109508e-03],
               [ 9.76334126e-03,  2.74741835e-02, -9.84441835e-02],
               [-2.84738787e-03,  2.82455574e-02, -8.46302365e-02]],
      
              [[ 1.76455902e-02,  3.48699330e-02, -1.12066834e-02],
               [ 2.56519386e-02,  3.03284960e-02,  2.70031257e-02],
               [ 8.51457640e-03,  1.04369079e-02,  3.20902969e-02],
               ...,
               [ 1.44325853e-02,  9.60955260e-03, -3.49045275e-02],
               [ 2.94730987e-02,  3.92554503e-02, -1.61254730e-02],
               [ 2.21664043e-02,  3.03301943e-02, -7.72575903e-03]]]])

    • obs_United Kingdom
      (chain, draw, obs_United Kingdom_dim_2, obs_United Kingdom_dim_3)
      float64
      0.0448 0.04243 ... 0.02593 0.05417

      array([[[[ 4.47963612e-02,  4.24337553e-02,  5.30809163e-02],
               [ 1.98628679e-02,  3.62871294e-02, -2.13912012e-02],
               [ 6.66614065e-03,  2.15867609e-02, -1.32673374e-02],
               ...,
               [ 4.31005695e-02,  3.91699840e-02,  6.53844859e-02],
               [ 4.41643424e-02,  2.77469541e-02,  7.85013753e-02],
               [ 3.93853453e-02,  3.28562568e-02,  8.88386060e-02]],
      
              [[-5.90061000e-03, -3.68935945e-03, -4.58361479e-03],
               [ 1.25872647e-03,  6.90687176e-03,  2.50108349e-02],
               [ 4.08323717e-02,  3.37580392e-02,  1.54248560e-01],
               ...,
               [ 4.08601546e-02,  2.69133667e-02,  1.37595011e-01],
               [ 3.98290375e-02,  2.03067542e-02,  4.83012601e-02],
               [ 1.56694518e-02,  1.62809715e-02,  4.68512624e-02]],
      
              [[ 3.01925836e-02,  1.73296171e-02,  7.20531325e-03],
               [ 1.73253627e-02,  2.25736782e-02,  5.78747659e-02],
               [-1.02540683e-02,  9.73991571e-04, -4.85102028e-02],
               ...,
      ...
               ...,
               [ 2.12890584e-03,  6.05849284e-03,  2.34878655e-02],
               [ 1.25287356e-02,  6.89032917e-03,  6.88012797e-02],
               [ 4.40254150e-03,  1.75809138e-03,  6.40606607e-03]],
      
              [[-1.73004397e-02, -7.43669461e-03, -2.15385541e-02],
               [-2.15727640e-03,  4.04738662e-03, -4.19487099e-02],
               [ 4.29180817e-02,  3.82009101e-02,  6.67301387e-02],
               ...,
               [-4.68188628e-03,  1.33528184e-02, -4.39221050e-02],
               [ 4.68646792e-02,  3.31468558e-02,  5.82560257e-02],
               [ 7.75585379e-03,  7.89267910e-03, -3.41566846e-02]],
      
              [[ 5.82243193e-02,  5.36666285e-02,  6.65792342e-02],
               [ 5.36896564e-02,  4.72045409e-02,  4.98576751e-02],
               [ 5.21386240e-02,  5.64919290e-02,  1.12981453e-01],
               ...,
               [ 3.53548206e-02,  2.98210067e-02,  1.94859678e-02],
               [ 2.80990148e-02,  3.17759443e-02, -9.36937590e-03],
               [ 2.15120699e-02,  2.59287536e-02,  5.41668008e-02]]]])

    • obs_United States
      (chain, draw, obs_United States_dim_2, obs_United States_dim_3)
      float64
      0.008293 0.0005756 ... 0.02601

      array([[[[ 0.00829273,  0.00057562,  0.00587833],
               [ 0.01323049,  0.00472613, -0.02500458],
               [ 0.01578798,  0.02120087,  0.01372787],
               ...,
               [ 0.00020075,  0.00101262, -0.0349095 ],
               [ 0.00136731,  0.00649784, -0.03638963],
               [ 0.04477031,  0.03937194,  0.05329405]],
      
              [[ 0.05196033,  0.03276444,  0.06056884],
               [ 0.02986291,  0.00465566,  0.10946823],
               [ 0.01320663,  0.01860797,  0.01033147],
               ...,
               [ 0.00389877,  0.00691071, -0.03040151],
               [ 0.00421392,  0.015716  ,  0.02244968],
               [ 0.01750093,  0.02115849,  0.01491858]],
      
              [[ 0.03202804,  0.0409238 ,  0.01360283],
               [-0.00775588,  0.01125095, -0.03788069],
               [ 0.01289303,  0.00459615,  0.01594723],
               ...,
      ...
               ...,
               [-0.00605736,  0.00638832, -0.01777219],
               [-0.0015468 ,  0.02003112, -0.03676623],
               [-0.01219943,  0.01533257, -0.04725824]],
      
              [[ 0.03360024,  0.03446592,  0.03699262],
               [-0.0141114 , -0.00257232, -0.06878331],
               [ 0.03911067,  0.04103395,  0.06795756],
               ...,
               [ 0.06179876,  0.04901743,  0.07049406],
               [ 0.00814458,  0.00760273,  0.00171805],
               [-0.03116158, -0.01415311, -0.11120307]],
      
              [[ 0.03732969,  0.02478824,  0.05976468],
               [ 0.01944701,  0.01566222,  0.04757722],
               [ 0.02900474,  0.04581697,  0.04853083],
               ...,
               [ 0.0171826 ,  0.01891361,  0.01726273],
               [ 0.01433668,  0.01098619,  0.04256221],
               [ 0.02656965,  0.02604265,  0.02600868]]]])

  • Indexes: (18)
    • chain
      PandasIndex

      PandasIndex(Int64Index([0, 1, 2, 3], dtype='int64', name='chain'))

    • draw
      PandasIndex

      PandasIndex(Int64Index([   0,    1,    2,    3,    4,    5,    6,    7,    8,    9,
                  ...
                  1990, 1991, 1992, 1993, 1994, 1995, 1996, 1997, 1998, 1999],
                 dtype='int64', name='draw', length=2000))

    • obs_Australia_dim_2
      PandasIndex

      PandasIndex(Int64Index([ 0,  1,  2,  3,  4,  5,  6,  7,  8,  9, 10, 11, 12, 13, 14, 15, 16,
                  17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33,
                  34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48],
                 dtype='int64', name='obs_Australia_dim_2'))

    • obs_Australia_dim_3
      PandasIndex

      PandasIndex(Int64Index([0, 1, 2], dtype='int64', name='obs_Australia_dim_3'))

    • obs_Canada_dim_2
      PandasIndex

      PandasIndex(Int64Index([0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18,
                  19, 20, 21],
                 dtype='int64', name='obs_Canada_dim_2'))

    • obs_Canada_dim_3
      PandasIndex

      PandasIndex(Int64Index([0, 1, 2], dtype='int64', name='obs_Canada_dim_3'))

    • obs_Chile_dim_2
      PandasIndex

      PandasIndex(Int64Index([ 0,  1,  2,  3,  4,  5,  6,  7,  8,  9, 10, 11, 12, 13, 14, 15, 16,
                  17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33,
                  34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48],
                 dtype='int64', name='obs_Chile_dim_2'))

    • obs_Chile_dim_3
      PandasIndex

      PandasIndex(Int64Index([0, 1, 2], dtype='int64', name='obs_Chile_dim_3'))

    • obs_Ireland_dim_2
      PandasIndex

      PandasIndex(Int64Index([ 0,  1,  2,  3,  4,  5,  6,  7,  8,  9, 10, 11, 12, 13, 14, 15, 16,
                  17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33,
                  34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48],
                 dtype='int64', name='obs_Ireland_dim_2'))

    • obs_Ireland_dim_3
      PandasIndex

      PandasIndex(Int64Index([0, 1, 2], dtype='int64', name='obs_Ireland_dim_3'))

    • obs_New Zealand_dim_2
      PandasIndex

      PandasIndex(Int64Index([ 0,  1,  2,  3,  4,  5,  6,  7,  8,  9, 10, 11, 12, 13, 14, 15, 16,
                  17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33,
                  34, 35, 36, 37, 38, 39, 40],
                 dtype='int64', name='obs_New Zealand_dim_2'))

    • obs_New Zealand_dim_3
      PandasIndex

      PandasIndex(Int64Index([0, 1, 2], dtype='int64', name='obs_New Zealand_dim_3'))

    • obs_South Africa_dim_2
      PandasIndex

      PandasIndex(Int64Index([ 0,  1,  2,  3,  4,  5,  6,  7,  8,  9, 10, 11, 12, 13, 14, 15, 16,
                  17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33,
                  34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48],
                 dtype='int64', name='obs_South Africa_dim_2'))

    • obs_South Africa_dim_3
      PandasIndex

      PandasIndex(Int64Index([0, 1, 2], dtype='int64', name='obs_South Africa_dim_3'))

    • obs_United Kingdom_dim_2
      PandasIndex

      PandasIndex(Int64Index([ 0,  1,  2,  3,  4,  5,  6,  7,  8,  9, 10, 11, 12, 13, 14, 15, 16,
                  17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33,
                  34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48],
                 dtype='int64', name='obs_United Kingdom_dim_2'))

    • obs_United Kingdom_dim_3
      PandasIndex

      PandasIndex(Int64Index([0, 1, 2], dtype='int64', name='obs_United Kingdom_dim_3'))

    • obs_United States_dim_2
      PandasIndex

      PandasIndex(Int64Index([ 0,  1,  2,  3,  4,  5,  6,  7,  8,  9, 10, 11, 12, 13, 14, 15, 16,
                  17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33,
                  34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45],
                 dtype='int64', name='obs_United States_dim_2'))

    • obs_United States_dim_3
      PandasIndex

      PandasIndex(Int64Index([0, 1, 2], dtype='int64', name='obs_United States_dim_3'))

  • Attributes: (4)

    created_at :

    2023-02-21T19:31:34.868405

    arviz_version :

    0.14.0

    inference_library :

    pymc

    inference_library_version :

    5.0.1

  
  
• sample_stats

  <xarray.Dataset>
  Dimensions:          (chain: 4, draw: 2000)
  Coordinates:
    * chain            (chain) int64 0 1 2 3
    * draw             (draw) int64 0 1 2 3 4 5 ... 1994 1995 1996 1997 1998 1999
  Data variables:
      lp               (chain, draw) float64 -2.64e+03 -2.628e+03 ... -2.604e+03
      diverging        (chain, draw) bool False False False ... False False False
      energy           (chain, draw) float64 -2.532e+03 -2.521e+03 ... -2.494e+03
      tree_depth       (chain, draw) int64 6 6 6 6 6 6 7 7 7 ... 6 6 6 5 6 6 6 6 6
      n_steps          (chain, draw) int64 63 63 63 63 63 63 ... 31 63 63 63 63 63
      acceptance_rate  (chain, draw) float64 0.8533 0.9783 ... 0.9693 0.9407
  Attributes:
      created_at:     2023-02-21T19:24:14.274886
      arviz_version:  0.14.0

  xarray.Dataset

  • Dimensions:
    • chain: 4
    • draw: 2000
  • Coordinates: (2)
    • chain
      (chain)
      int64
      0 1 2 3

      array([0, 1, 2, 3])

    • draw
      (draw)
      int64
      0 1 2 3 4 ... 1996 1997 1998 1999

      array([   0,    1,    2, ..., 1997, 1998, 1999])

  • Data variables: (6)
    • lp
      (chain, draw)
      float64
      -2.64e+03 -2.628e+03 ... -2.604e+03

      array([[-2639.89115833, -2627.55770592, -2634.71443207, ...,
              -2765.56713392, -2748.95428527, -2735.7959319 ],
             [-2561.93945366, -2572.71071931, -2564.66514406, ...,
              -2616.41390537, -2618.61317438, -2623.36681425],
             [-2618.62600932, -2634.94074369, -2642.66539056, ...,
              -2653.05805478, -2656.48474006, -2651.63628297],
             [-2643.62426065, -2633.29142627, -2611.0879038 , ...,
              -2634.38375437, -2629.36058901, -2603.85800117]])

    • diverging
      (chain, draw)
      bool
      False False False ... False False

      array([[False, False, False, ..., False, False, False],
             [False, False, False, ..., False, False, False],
             [False, False, False, ..., False, False, False],
             [False, False, False, ..., False, False, False]])

    • energy
      (chain, draw)
      float64
      -2.532e+03 ... -2.494e+03

      array([[-2531.58065155, -2521.32883239, -2514.6890569 , ...,
              -2630.50082991, -2637.8246221 , -2628.53079807],
             [-2441.12079867, -2432.56725591, -2440.74362316, ...,
              -2522.43066788, -2496.14911007, -2504.88809094],
             [-2492.78271971, -2519.36678959, -2519.07385537, ...,
              -2533.16366468, -2536.07235735, -2540.30849264],
             [-2521.35037416, -2507.4984581 , -2497.56736915, ...,
              -2527.36637866, -2511.02585969, -2493.66140801]])

    • tree_depth
      (chain, draw)
      int64
      6 6 6 6 6 6 7 7 ... 6 6 5 6 6 6 6 6

      array([[6, 6, 6, ..., 6, 6, 6],
             [7, 7, 7, ..., 6, 7, 6],
             [6, 6, 6, ..., 6, 6, 6],
             [6, 6, 6, ..., 6, 6, 6]])

    • n_steps
      (chain, draw)
      int64
      63 63 63 63 63 ... 63 63 63 63 63

      array([[ 63,  63,  63, ...,  63,  63,  63],
             [127, 127, 127, ...,  63, 127,  63],
             [ 63,  63,  63, ...,  63,  63,  63],
             [ 63,  63,  63, ...,  63,  63,  63]])

    • acceptance_rate
      (chain, draw)
      float64
      0.8533 0.9783 ... 0.9693 0.9407

      array([[0.85333103, 0.97828366, 0.96105869, ..., 0.98549555, 0.97487632,
              0.67458368],
             [0.95142328, 0.99429708, 0.81421262, ..., 0.97399939, 0.81520905,
              0.97292531],
             [0.92793643, 0.25595475, 0.9103398 , ..., 0.95571164, 0.74282113,
              0.99596529],
             [0.99370679, 0.92069916, 0.8585449 , ..., 0.46255423, 0.96933128,
              0.94071658]])

  • Indexes: (2)
    • chain
      PandasIndex

      PandasIndex(Int64Index([0, 1, 2, 3], dtype='int64', name='chain'))

    • draw
      PandasIndex

      PandasIndex(Int64Index([   0,    1,    2,    3,    4,    5,    6,    7,    8,    9,
                  ...
                  1990, 1991, 1992, 1993, 1994, 1995, 1996, 1997, 1998, 1999],
                 dtype='int64', name='draw', length=2000))

  • Attributes: (2)

    created_at :

    2023-02-21T19:24:14.274886

    arviz_version :

    0.14.0

  
  
• prior

  <xarray.Dataset>
  Dimensions:                               (chain: 1, draw: 500,
                                             omega_global_dim_0: 6,
                                             betaX_Canada_dim_0: 22,
                                             betaX_Canada_dim_1: 3,
                                             noise_chol_South Africa_dim_0: 6,
                                             omega_New Zealand_dim_0: 3,
                                             ...
                                             noise_chol_New Zealand_corr_dim_0: 3,
                                             noise_chol_New Zealand_corr_dim_1: 3,
                                             noise_chol_United States_corr_dim_0: 3,
                                             noise_chol_United States_corr_dim_1: 3,
                                             noise_chol_Chile_dim_0: 6,
                                             noise_chol_Ireland_stds_dim_0: 3)
  Coordinates: (12/73)
    * chain                                 (chain) int64 0
    * draw                                  (draw) int64 0 1 2 3 ... 497 498 499
    * omega_global_dim_0                    (omega_global_dim_0) int64 0 1 2 3 4 5
    * betaX_Canada_dim_0                    (betaX_Canada_dim_0) int64 0 1 ... 21
    * betaX_Canada_dim_1                    (betaX_Canada_dim_1) int64 0 1 2
    * noise_chol_South Africa_dim_0         (noise_chol_South Africa_dim_0) int64 ...
      ...                                    ...
    * noise_chol_New Zealand_corr_dim_0     (noise_chol_New Zealand_corr_dim_0) int64 ...
    * noise_chol_New Zealand_corr_dim_1     (noise_chol_New Zealand_corr_dim_1) int64 ...
    * noise_chol_United States_corr_dim_0   (noise_chol_United States_corr_dim_0) int64 ...
    * noise_chol_United States_corr_dim_1   (noise_chol_United States_corr_dim_1) int64 ...
    * noise_chol_Chile_dim_0                (noise_chol_Chile_dim_0) int64 0 ... 5
    * noise_chol_Ireland_stds_dim_0         (noise_chol_Ireland_stds_dim_0) int64 ...
  Data variables: (12/80)
      omega_global                          (chain, draw, omega_global_dim_0) float64 ...
      betaX_Canada                          (chain, draw, betaX_Canada_dim_0, betaX_Canada_dim_1) float64 ...
      noise_chol_South Africa               (chain, draw, noise_chol_South Africa_dim_0) float64 ...
      omega_New Zealand                     (chain, draw, omega_New Zealand_dim_0, omega_New Zealand_dim_1) float64 ...
      lag_coefs_United States               (chain, draw, equations, lags, cross_vars) float64 ...
      betaX_United States                   (chain, draw, betaX_United States_dim_0, betaX_United States_dim_1) float64 ...
      ...                                    ...
      noise_chol_Chile                      (chain, draw, noise_chol_Chile_dim_0) float64 ...
      z_scale_alpha_United States           (chain, draw) float64 0.2131 ... 0....
      noise_chol_Ireland_stds               (chain, draw, noise_chol_Ireland_stds_dim_0) float64 ...
      beta_hat_location                     (chain, draw) float64 -0.1648 ... 0...
      rho                                   (chain, draw) float64 0.4541 ... 0....
      z_scale_alpha_Canada                  (chain, draw) float64 0.06378 ... 0...
  Attributes:
      created_at:                 2023-02-21T19:22:35.383920
      arviz_version:              0.14.0
      inference_library:          pymc
      inference_library_version:  5.0.1

  xarray.Dataset

  • Dimensions:
    • chain: 1
    • draw: 500
    • omega_global_dim_0: 6
    • betaX_Canada_dim_0: 22
    • betaX_Canada_dim_1: 3
    • noise_chol_South Africa_dim_0: 6
    • omega_New Zealand_dim_0: 3
    • omega_New Zealand_dim_1: 3
    • equations: 3
    • lags: 2
    • cross_vars: 3
    • betaX_United States_dim_0: 46
    • betaX_United States_dim_1: 3
    • noise_chol_United Kingdom_stds_dim_0: 3
    • noise_chol_New Zealand_stds_dim_0: 3
    • omega_United Kingdom_dim_0: 3
    • omega_United Kingdom_dim_1: 3
    • omega_Australia_dim_0: 3
    • omega_Australia_dim_1: 3
    • noise_chol_South Africa_stds_dim_0: 3
    • omega_Ireland_dim_0: 3
    • omega_Ireland_dim_1: 3
    • noise_chol_Chile_corr_dim_0: 3
    • noise_chol_Chile_corr_dim_1: 3
    • noise_chol_United States_stds_dim_0: 3
    • omega_United States_dim_0: 3
    • omega_United States_dim_1: 3
    • noise_chol_New Zealand_dim_0: 6
    • omega_Chile_dim_0: 3
    • omega_Chile_dim_1: 3
    • noise_chol_United States_dim_0: 6
    • noise_chol_United Kingdom_corr_dim_0: 3
    • noise_chol_United Kingdom_corr_dim_1: 3
    • betaX_United Kingdom_dim_0: 49
    • betaX_United Kingdom_dim_1: 3
    • betaX_Ireland_dim_0: 49
    • betaX_Ireland_dim_1: 3
    • omega_South Africa_dim_0: 3
    • omega_South Africa_dim_1: 3
    • noise_chol_Canada_dim_0: 6
    • omega_global_corr_dim_0: 3
    • omega_global_corr_dim_1: 3
    • betaX_Australia_dim_0: 49
    • betaX_Australia_dim_1: 3
    • noise_chol_Canada_corr_dim_0: 3
    • noise_chol_Canada_corr_dim_1: 3
    • noise_chol_Chile_stds_dim_0: 3
    • noise_chol_United Kingdom_dim_0: 6
    • noise_chol_Australia_dim_0: 6
    • betaX_New Zealand_dim_0: 41
    • betaX_New Zealand_dim_1: 3
    • noise_chol_Australia_corr_dim_0: 3
    • noise_chol_Australia_corr_dim_1: 3
    • omega_Canada_dim_0: 3
    • omega_Canada_dim_1: 3
    • noise_chol_Australia_stds_dim_0: 3
    • noise_chol_South Africa_corr_dim_0: 3
    • noise_chol_South Africa_corr_dim_1: 3
    • noise_chol_Ireland_dim_0: 6
    • noise_chol_Ireland_corr_dim_0: 3
    • noise_chol_Ireland_corr_dim_1: 3
    • betaX_Chile_dim_0: 49
    • betaX_Chile_dim_1: 3
    • omega_global_stds_dim_0: 3
    • betaX_South Africa_dim_0: 49
    • betaX_South Africa_dim_1: 3
    • noise_chol_Canada_stds_dim_0: 3
    • noise_chol_New Zealand_corr_dim_0: 3
    • noise_chol_New Zealand_corr_dim_1: 3
    • noise_chol_United States_corr_dim_0: 3
    • noise_chol_United States_corr_dim_1: 3
    • noise_chol_Chile_dim_0: 6
    • noise_chol_Ireland_stds_dim_0: 3
  • Coordinates: (73)
    • chain
      (chain)
      int64
      0

      array([0])

    • draw
      (draw)
      int64
      0 1 2 3 4 5 ... 495 496 497 498 499

      array([  0,   1,   2, ..., 497, 498, 499])

    • omega_global_dim_0
      (omega_global_dim_0)
      int64
      0 1 2 3 4 5

      array([0, 1, 2, 3, 4, 5])

    • betaX_Canada_dim_0
      (betaX_Canada_dim_0)
      int64
      0 1 2 3 4 5 6 ... 16 17 18 19 20 21

      array([ 0,  1,  2,  3,  4,  5,  6,  7,  8,  9, 10, 11, 12, 13, 14, 15, 16, 17,
             18, 19, 20, 21])

    • betaX_Canada_dim_1
      (betaX_Canada_dim_1)
      int64
      0 1 2

      array([0, 1, 2])

    • noise_chol_South Africa_dim_0
      (noise_chol_South Africa_dim_0)
      int64
      0 1 2 3 4 5

      array([0, 1, 2, 3, 4, 5])

    • omega_New Zealand_dim_0
      (omega_New Zealand_dim_0)
      int64
      0 1 2

      array([0, 1, 2])

    • omega_New Zealand_dim_1
      (omega_New Zealand_dim_1)
      int64
      0 1 2

      array([0, 1, 2])

    • equations
      (equations)
      <U7
      'dl_gdp' 'dl_cons' 'dl_gfcf'

      array(['dl_gdp', 'dl_cons', 'dl_gfcf'], dtype='<U7')

    • lags
      (lags)
      int64
      1 2

      array([1, 2])

    • cross_vars
      (cross_vars)
      <U7
      'dl_gdp' 'dl_cons' 'dl_gfcf'

      array(['dl_gdp', 'dl_cons', 'dl_gfcf'], dtype='<U7')

    • betaX_United States_dim_0
      (betaX_United States_dim_0)
      int64
      0 1 2 3 4 5 6 ... 40 41 42 43 44 45

      array([ 0,  1,  2,  3,  4,  5,  6,  7,  8,  9, 10, 11, 12, 13, 14, 15, 16, 17,
             18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35,
             36, 37, 38, 39, 40, 41, 42, 43, 44, 45])

    • betaX_United States_dim_1
      (betaX_United States_dim_1)
      int64
      0 1 2

      array([0, 1, 2])

    • noise_chol_United Kingdom_stds_dim_0
      (noise_chol_United Kingdom_stds_dim_0)
      int64
      0 1 2

      array([0, 1, 2])

    • noise_chol_New Zealand_stds_dim_0
      (noise_chol_New Zealand_stds_dim_0)
      int64
      0 1 2

      array([0, 1, 2])

    • omega_United Kingdom_dim_0
      (omega_United Kingdom_dim_0)
      int64
      0 1 2

      array([0, 1, 2])

    • omega_United Kingdom_dim_1
      (omega_United Kingdom_dim_1)
      int64
      0 1 2

      array([0, 1, 2])

    • omega_Australia_dim_0
      (omega_Australia_dim_0)
      int64
      0 1 2

      array([0, 1, 2])

    • omega_Australia_dim_1
      (omega_Australia_dim_1)
      int64
      0 1 2

      array([0, 1, 2])

    • noise_chol_South Africa_stds_dim_0
      (noise_chol_South Africa_stds_dim_0)
      int64
      0 1 2

      array([0, 1, 2])

    • omega_Ireland_dim_0
      (omega_Ireland_dim_0)
      int64
      0 1 2

      array([0, 1, 2])

    • omega_Ireland_dim_1
      (omega_Ireland_dim_1)
      int64
      0 1 2

      array([0, 1, 2])

    • noise_chol_Chile_corr_dim_0
      (noise_chol_Chile_corr_dim_0)
      int64
      0 1 2

      array([0, 1, 2])

    • noise_chol_Chile_corr_dim_1
      (noise_chol_Chile_corr_dim_1)
      int64
      0 1 2

      array([0, 1, 2])

    • noise_chol_United States_stds_dim_0
      (noise_chol_United States_stds_dim_0)
      int64
      0 1 2

      array([0, 1, 2])

    • omega_United States_dim_0
      (omega_United States_dim_0)
      int64
      0 1 2

      array([0, 1, 2])

    • omega_United States_dim_1
      (omega_United States_dim_1)
      int64
      0 1 2

      array([0, 1, 2])

    • noise_chol_New Zealand_dim_0
      (noise_chol_New Zealand_dim_0)
      int64
      0 1 2 3 4 5

      array([0, 1, 2, 3, 4, 5])

    • omega_Chile_dim_0
      (omega_Chile_dim_0)
      int64
      0 1 2

      array([0, 1, 2])

    • omega_Chile_dim_1
      (omega_Chile_dim_1)
      int64
      0 1 2

      array([0, 1, 2])

    • noise_chol_United States_dim_0
      (noise_chol_United States_dim_0)
      int64
      0 1 2 3 4 5

      array([0, 1, 2, 3, 4, 5])

    • noise_chol_United Kingdom_corr_dim_0
      (noise_chol_United Kingdom_corr_dim_0)
      int64
      0 1 2

      array([0, 1, 2])

    • noise_chol_United Kingdom_corr_dim_1
      (noise_chol_United Kingdom_corr_dim_1)
      int64
      0 1 2

      array([0, 1, 2])

    • betaX_United Kingdom_dim_0
      (betaX_United Kingdom_dim_0)
      int64
      0 1 2 3 4 5 6 ... 43 44 45 46 47 48

      array([ 0,  1,  2,  3,  4,  5,  6,  7,  8,  9, 10, 11, 12, 13, 14, 15, 16, 17,
             18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35,
             36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48])

    • betaX_United Kingdom_dim_1
      (betaX_United Kingdom_dim_1)
      int64
      0 1 2

      array([0, 1, 2])

    • betaX_Ireland_dim_0
      (betaX_Ireland_dim_0)
      int64
      0 1 2 3 4 5 6 ... 43 44 45 46 47 48

      array([ 0,  1,  2,  3,  4,  5,  6,  7,  8,  9, 10, 11, 12, 13, 14, 15, 16, 17,
             18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35,
             36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48])

    • betaX_Ireland_dim_1
      (betaX_Ireland_dim_1)
      int64
      0 1 2

      array([0, 1, 2])

    • omega_South Africa_dim_0
      (omega_South Africa_dim_0)
      int64
      0 1 2

      array([0, 1, 2])

    • omega_South Africa_dim_1
      (omega_South Africa_dim_1)
      int64
      0 1 2

      array([0, 1, 2])

    • noise_chol_Canada_dim_0
      (noise_chol_Canada_dim_0)
      int64
      0 1 2 3 4 5

      array([0, 1, 2, 3, 4, 5])

    • omega_global_corr_dim_0
      (omega_global_corr_dim_0)
      int64
      0 1 2

      array([0, 1, 2])

    • omega_global_corr_dim_1
      (omega_global_corr_dim_1)
      int64
      0 1 2

      array([0, 1, 2])

    • betaX_Australia_dim_0
      (betaX_Australia_dim_0)
      int64
      0 1 2 3 4 5 6 ... 43 44 45 46 47 48

      array([ 0,  1,  2,  3,  4,  5,  6,  7,  8,  9, 10, 11, 12, 13, 14, 15, 16, 17,
             18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35,
             36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48])

    • betaX_Australia_dim_1
      (betaX_Australia_dim_1)
      int64
      0 1 2

      array([0, 1, 2])

    • noise_chol_Canada_corr_dim_0
      (noise_chol_Canada_corr_dim_0)
      int64
      0 1 2

      array([0, 1, 2])

    • noise_chol_Canada_corr_dim_1
      (noise_chol_Canada_corr_dim_1)
      int64
      0 1 2

      array([0, 1, 2])

    • noise_chol_Chile_stds_dim_0
      (noise_chol_Chile_stds_dim_0)
      int64
      0 1 2

      array([0, 1, 2])

    • noise_chol_United Kingdom_dim_0
      (noise_chol_United Kingdom_dim_0)
      int64
      0 1 2 3 4 5

      array([0, 1, 2, 3, 4, 5])

    • noise_chol_Australia_dim_0
      (noise_chol_Australia_dim_0)
      int64
      0 1 2 3 4 5

      array([0, 1, 2, 3, 4, 5])

    • betaX_New Zealand_dim_0
      (betaX_New Zealand_dim_0)
      int64
      0 1 2 3 4 5 6 ... 35 36 37 38 39 40

      array([ 0,  1,  2,  3,  4,  5,  6,  7,  8,  9, 10, 11, 12, 13, 14, 15, 16, 17,
             18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35,
             36, 37, 38, 39, 40])

    • betaX_New Zealand_dim_1
      (betaX_New Zealand_dim_1)
      int64
      0 1 2

      array([0, 1, 2])

    • noise_chol_Australia_corr_dim_0
      (noise_chol_Australia_corr_dim_0)
      int64
      0 1 2

      array([0, 1, 2])

    • noise_chol_Australia_corr_dim_1
      (noise_chol_Australia_corr_dim_1)
      int64
      0 1 2

      array([0, 1, 2])

    • omega_Canada_dim_0
      (omega_Canada_dim_0)
      int64
      0 1 2

      array([0, 1, 2])

    • omega_Canada_dim_1
      (omega_Canada_dim_1)
      int64
      0 1 2

      array([0, 1, 2])

    • noise_chol_Australia_stds_dim_0
      (noise_chol_Australia_stds_dim_0)
      int64
      0 1 2

      array([0, 1, 2])

    • noise_chol_South Africa_corr_dim_0
      (noise_chol_South Africa_corr_dim_0)
      int64
      0 1 2

      array([0, 1, 2])

    • noise_chol_South Africa_corr_dim_1
      (noise_chol_South Africa_corr_dim_1)
      int64
      0 1 2

      array([0, 1, 2])

    • noise_chol_Ireland_dim_0
      (noise_chol_Ireland_dim_0)
      int64
      0 1 2 3 4 5

      array([0, 1, 2, 3, 4, 5])

    • noise_chol_Ireland_corr_dim_0
      (noise_chol_Ireland_corr_dim_0)
      int64
      0 1 2

      array([0, 1, 2])

    • noise_chol_Ireland_corr_dim_1
      (noise_chol_Ireland_corr_dim_1)
      int64
      0 1 2

      array([0, 1, 2])

    • betaX_Chile_dim_0
      (betaX_Chile_dim_0)
      int64
      0 1 2 3 4 5 6 ... 43 44 45 46 47 48

      array([ 0,  1,  2,  3,  4,  5,  6,  7,  8,  9, 10, 11, 12, 13, 14, 15, 16, 17,
             18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35,
             36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48])

    • betaX_Chile_dim_1
      (betaX_Chile_dim_1)
      int64
      0 1 2

      array([0, 1, 2])

    • omega_global_stds_dim_0
      (omega_global_stds_dim_0)
      int64
      0 1 2

      array([0, 1, 2])

    • betaX_South Africa_dim_0
      (betaX_South Africa_dim_0)
      int64
      0 1 2 3 4 5 6 ... 43 44 45 46 47 48

      array([ 0,  1,  2,  3,  4,  5,  6,  7,  8,  9, 10, 11, 12, 13, 14, 15, 16, 17,
             18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35,
             36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48])

    • betaX_South Africa_dim_1
      (betaX_South Africa_dim_1)
      int64
      0 1 2

      array([0, 1, 2])

    • noise_chol_Canada_stds_dim_0
      (noise_chol_Canada_stds_dim_0)
      int64
      0 1 2

      array([0, 1, 2])

    • noise_chol_New Zealand_corr_dim_0
      (noise_chol_New Zealand_corr_dim_0)
      int64
      0 1 2

      array([0, 1, 2])

    • noise_chol_New Zealand_corr_dim_1
      (noise_chol_New Zealand_corr_dim_1)
      int64
      0 1 2

      array([0, 1, 2])

    • noise_chol_United States_corr_dim_0
      (noise_chol_United States_corr_dim_0)
      int64
      0 1 2

      array([0, 1, 2])

    • noise_chol_United States_corr_dim_1
      (noise_chol_United States_corr_dim_1)
      int64
      0 1 2

      array([0, 1, 2])

    • noise_chol_Chile_dim_0
      (noise_chol_Chile_dim_0)
      int64
      0 1 2 3 4 5

      array([0, 1, 2, 3, 4, 5])

    • noise_chol_Ireland_stds_dim_0
      (noise_chol_Ireland_stds_dim_0)
      int64
      0 1 2

      array([0, 1, 2])

  • Data variables: (80)
    • omega_global
      (chain, draw, omega_global_dim_0)
      float64
      2.027 0.1165 ... -0.05625 1.081

      array([[[ 2.02687573,  0.11647196,  0.37456589, -0.05392265,
                0.04851504,  0.19494854],
              [ 1.42338109, -0.7031298 ,  1.20526889, -1.10723708,
               -0.56268989,  0.16130681],
              [ 0.17172083,  0.13656726,  0.37594241,  0.03902472,
               -0.33701542,  0.3199291 ],
              ...,
              [ 0.49741775, -0.06073033,  0.21288268,  0.04606727,
               -0.26836034,  0.32224374],
              [ 4.03165864, -1.5451338 ,  1.51594275, -0.09386334,
               -0.09212436,  0.06404812],
              [ 2.50023366,  2.99005488,  0.38783897,  0.54857007,
               -0.05625022,  1.08114627]]])

    • betaX_Canada
      (chain, draw, betaX_Canada_dim_0, betaX_Canada_dim_1)
      float64
      -0.02959 -0.03111 ... -0.004869

      array([[[[-0.02958802, -0.03111391, -0.02964134],
               [-0.03755296, -0.04026266, -0.03852361],
               [-0.03670091, -0.03886219, -0.03409941],
               ...,
               [-0.0257217 , -0.02779475, -0.02744646],
               [-0.01794688, -0.0182232 , -0.02087961],
               [ 0.00436016,  0.00622635,  0.00900255]],
      
              [[-0.0425969 , -0.04366728, -0.04615484],
               [-0.05258459, -0.05409159, -0.05866094],
               [-0.04568509, -0.04411511, -0.05134403],
               ...,
               [-0.03367277, -0.03391679, -0.03839855],
               [-0.02211253, -0.02176753, -0.02595201],
               [ 0.01687551,  0.02297411,  0.01621278]],
      
              [[ 0.03378103,  0.0338103 ,  0.03402627],
               [ 0.04220881,  0.04225048,  0.04234694],
               [ 0.03633951,  0.03654703,  0.03637642],
               ...,
      ...
               ...,
               [-0.03480167, -0.03707513, -0.03885839],
               [-0.02075958, -0.02547082, -0.02567666],
               [ 0.01950194,  0.01199164,  0.01058504]],
      
              [[-0.00426948,  0.00734552, -0.00132585],
               [-0.00391059,  0.00958301, -0.00163274],
               [-0.00091696,  0.0074017 ,  0.00137115],
               ...,
               [-0.00132751,  0.00584341, -0.00113681],
               [-0.00041472,  0.00370545, -0.00094243],
               [ 0.00809292, -0.00379171,  0.00419078]],
      
              [[ 0.01158302,  0.01273005,  0.01295267],
               [ 0.01457555,  0.01590839,  0.01613327],
               [ 0.01244839,  0.01370919,  0.01421059],
               ...,
               [ 0.00943236,  0.01019738,  0.01032848],
               [ 0.00635713,  0.00661155,  0.00668655],
               [-0.004658  , -0.00547512, -0.00486891]]]])

    • noise_chol_South Africa
      (chain, draw, noise_chol_South Africa_dim_0)
      float64
      1.581 0.2351 ... -0.06042 0.1807

      array([[[ 1.58122840e+00,  2.35063162e-01,  1.81065326e+00,
                6.69361180e-03, -2.60958004e-03,  3.70879685e-02],
              [ 3.29713432e+00,  3.28705752e-02,  3.23124184e-01,
                3.28256261e-01, -5.83091202e-01,  2.81468551e+00],
              [ 8.70964317e-01, -1.50781168e-01,  6.64077957e-01,
               -7.27371344e-02, -1.63955244e-03,  1.80082914e+00],
              ...,
              [ 6.62529343e-01, -2.23523154e-01,  1.85091748e+00,
                6.98613335e-01, -2.89741836e-02,  2.05858881e+00],
              [ 2.86182017e-01,  9.22905260e-02,  7.41981134e-01,
                4.80310851e-04,  1.42592625e-01,  5.47812994e-01],
              [ 1.61046635e-01,  8.23376815e-02,  3.18195594e-01,
                2.28347316e-02, -6.04202178e-02,  1.80685825e-01]]])

    • omega_New Zealand
      (chain, draw, omega_New Zealand_dim_0, omega_New Zealand_dim_1)
      float64
      1.235 0.0 0.0 ... -0.05175 0.8164

      array([[[[ 1.23475989,  0.        ,  0.        ],
               [ 0.05707809,  0.18012104,  0.        ],
               [ 0.12814648, -0.14911574,  0.62815169]],
      
              [[ 1.12848127,  0.        ,  0.        ],
               [-0.4626681 ,  1.00359328,  0.        ],
               [-0.78412303, -0.38860358,  0.12772782]],
      
              [[ 0.3386176 ,  0.        ,  0.        ],
               [ 0.11565954,  1.97196896,  0.        ],
               [ 0.05263391, -0.35786357,  0.85787868]],
      
              ...,
      
              [[ 0.38447676,  0.        ,  0.        ],
               [-0.14655631,  0.63812057,  0.        ],
               [-0.351443  , -0.05787807,  1.01881844]],
      
              [[ 1.62221937,  0.        ,  0.        ],
               [-0.22344884,  0.8221504 ,  0.        ],
               [ 0.44877203, -0.3211205 ,  1.60225819]],
      
              [[ 1.65910263,  0.        ,  0.        ],
               [ 1.69784562,  0.43286907,  0.        ],
               [ 0.32013471, -0.05175294,  0.81644111]]]])

    • lag_coefs_United States
      (chain, draw, equations, lags, cross_vars)
      float64
      -0.1935 -0.2252 ... 0.06284 0.05233

      array([[[[[-0.19351   , -0.22521912, -0.1517748 ],
                [-0.24910903,  0.00387421, -0.07808006]],
      
               [[-0.21532541, -0.2332341 , -0.36174169],
                [-0.15914035, -0.19475919, -0.07084988]],
      
               [[-0.08980639, -0.12722645, -0.1085578 ],
                [-0.30059753, -0.20408448, -0.1545564 ]]],
      
      
              [[[-0.18886062, -0.17840099, -0.21103498],
                [-0.21810999, -0.20734971, -0.20962268]],
      
               [[-0.18253502, -0.20026692, -0.20777754],
                [-0.20243412, -0.21968197, -0.18696931]],
      
               [[-0.15498564, -0.19470107, -0.20251693],
                [-0.19547364, -0.17793239, -0.21758384]]],
      
      
      ...
      
      
              [[[ 0.04566002,  0.04279759,  0.01117736],
                [-0.02671817,  0.04126656, -0.01548748]],
      
               [[ 0.04193849,  0.02128232, -0.19083049],
                [ 0.00676198,  0.02390407, -0.02639729]],
      
               [[ 0.13080941,  0.02435788, -0.00379633],
                [ 0.12300067,  0.04885043,  0.05568541]]],
      
      
              [[[ 0.05033085,  0.06261057,  0.05781419],
                [ 0.06337439,  0.05412811,  0.06496625]],
      
               [[ 0.0511598 ,  0.06752266,  0.07029739],
                [ 0.06096998,  0.05747771,  0.05488061]],
      
               [[ 0.067718  ,  0.07093895,  0.05849658],
                [ 0.05365325,  0.06284001,  0.05232967]]]]])

    • betaX_United States
      (chain, draw, betaX_United States_dim_0, betaX_United States_dim_1)
      float64
      -0.01138 -0.004519 ... 0.01024

      array([[[[-0.01137667, -0.00451903, -0.02929914],
               [ 0.01122024,  0.02658823,  0.01367127],
               [-0.02489871, -0.04786618, -0.01080599],
               ...,
               [-0.02015653, -0.03168506, -0.02160832],
               [-0.02624333, -0.03773096, -0.02704752],
               [-0.02427429, -0.03359497, -0.02858871]],
      
              [[-0.02393938, -0.0220922 , -0.02268617],
               [ 0.02222772,  0.02050507,  0.02128093],
               [-0.02215843, -0.02453128, -0.01918522],
               ...,
               [-0.02854824, -0.02827249, -0.02690168],
               [-0.0358828 , -0.03516884, -0.03417038],
               [-0.03514358, -0.0342643 , -0.03339847]],
      
              [[ 0.01788564,  0.01799546,  0.02211616],
               [-0.01804569, -0.01675939, -0.01407074],
               [ 0.02058391,  0.02098643,  0.01705385],
               ...,
      ...
               ...,
               [-0.02512259, -0.03356722, -0.02451416],
               [-0.03030195, -0.04144246, -0.02974323],
               [-0.02848949, -0.03989498, -0.02828534]],
      
              [[-0.00182867,  0.00674854,  0.01169921],
               [ 0.00072007,  0.01583485, -0.00239951],
               [ 0.00724176, -0.00910908,  0.00424258],
               ...,
               [ 0.00248719, -0.00567769,  0.00761097],
               [ 0.00253376, -0.00677438,  0.01002803],
               [ 0.00192006, -0.00478675,  0.01053876]],
      
              [[ 0.00715985,  0.00594686,  0.00593528],
               [-0.00608821, -0.00651577, -0.00544604],
               [ 0.00593823,  0.008     ,  0.00843259],
               ...,
               [ 0.00821864,  0.008629  ,  0.00857489],
               [ 0.01045224,  0.01077109,  0.01067808],
               [ 0.01024788,  0.01034098,  0.01024373]]]])

    • z_scale_alpha_Ireland
      (chain, draw)
      float64
      0.5116 0.1397 ... 0.1342 0.2306

      array([[0.51158645, 0.13970817, 0.09375044, 0.22546456, 0.11690336,
              0.18071698, 0.13085104, 0.12613609, 0.11071867, 0.11863399,
              1.01966015, 0.08379751, 0.35997548, 0.09879424, 0.14538562,
              0.24479192, 0.32613972, 0.34103393, 0.09204398, 0.15258833,
              0.0846486 , 0.16851581, 0.22037281, 0.43876369, 0.27917013,
              0.28890463, 0.36907312, 0.06880731, 0.32653339, 0.16650296,
              0.67233228, 0.17520708, 0.73168596, 0.17943095, 0.04339154,
              0.87860528, 0.0902929 , 0.12554086, 0.05205397, 0.13163887,
              0.18812767, 0.28784634, 0.12096629, 0.28414731, 0.30588849,
              0.08410933, 0.16007233, 0.07836366, 0.25604716, 0.22755973,
              0.08053769, 0.10195325, 0.15135842, 0.23905198, 0.17683231,
              0.20688851, 0.16360327, 0.16471266, 0.60683626, 0.41665465,
              0.20856958, 0.09474701, 0.17649755, 0.26976955, 0.13058694,
              0.22029265, 0.23742807, 0.57035641, 0.1317696 , 0.19482831,
              0.19729133, 0.33593179, 0.11966043, 0.13913473, 0.08842925,
              0.16272767, 0.09280604, 3.47688008, 0.1381783 , 0.12320211,
              0.30030345, 0.31766401, 0.69338639, 0.20337742, 0.2342212 ,
              0.18209416, 0.7522726 , 0.19758033, 0.76945964, 0.31365889,
              0.12344788, 0.76560755, 0.24752784, 0.25957989, 0.09198846,
              0.34464921, 0.37336806, 0.10254146, 0.16931808, 0.10916805,
      ...
              0.15973534, 1.17441072, 0.19365826, 0.08147133, 0.16842842,
              0.35135656, 0.09271101, 0.14803967, 0.21271489, 0.17090407,
              1.31439143, 0.19568287, 0.1324949 , 0.7336209 , 0.08684975,
              0.30756519, 0.28528399, 0.61887749, 0.37268476, 0.08006531,
              0.26596824, 0.10191996, 0.23494502, 0.73125934, 0.16135043,
              0.31041881, 0.24232558, 0.23723761, 0.29023683, 0.27058875,
              0.12401297, 0.11695787, 0.13830657, 0.16463358, 0.20700472,
              0.14013282, 0.16698267, 0.26857147, 0.18290139, 0.18879111,
              0.14139622, 0.20556509, 0.11803317, 0.13828638, 0.10692438,
              0.07661694, 0.61984467, 0.22950678, 0.52285373, 0.26827668,
              0.27439876, 0.2871008 , 0.0865294 , 0.16514618, 0.11516385,
              0.19218968, 0.14700579, 0.58597846, 0.17383473, 0.09574533,
              0.35871119, 0.1845075 , 0.14243374, 0.19698913, 0.24377526,
              0.41340451, 0.23316587, 0.13564413, 0.2755567 , 0.62852515,
              0.26603256, 0.07591389, 0.14888167, 0.5318431 , 0.15210543,
              0.13585047, 0.41461438, 0.31654239, 0.18930941, 0.5823387 ,
              0.13762684, 0.16860118, 0.10612805, 0.18198135, 0.15497983,
              0.14827952, 0.08008737, 0.07503787, 0.16820413, 0.06952973,
              0.43373073, 0.1333964 , 0.20756783, 0.23637012, 0.11010225,
              0.22196761, 0.2610846 , 0.65380877, 0.13424296, 0.23055266]])

    • z_scale_beta_United States
      (chain, draw)
      float64
      0.2073 0.07694 ... 0.242 0.1381

      array([[0.20734036, 0.07693513, 0.18672826, 0.19813901, 0.22038334,
              0.16681774, 0.22328428, 0.26010326, 0.2193448 , 1.88297581,
              0.11857573, 0.19167814, 0.17406328, 0.2120837 , 0.29897147,
              0.1438986 , 0.5631577 , 0.10040927, 0.14017919, 0.14549112,
              0.17853873, 0.47852713, 0.15319318, 0.28302628, 0.17486913,
              0.29753298, 0.67343941, 0.30223281, 0.20796031, 0.32657908,
              0.15982154, 0.07102473, 0.11100181, 0.19291736, 0.11073926,
              0.26723373, 0.12051404, 0.17071922, 0.08569388, 0.1487173 ,
              0.68398926, 1.44224934, 0.07962882, 0.13715676, 0.20909543,
              0.41409616, 0.29805412, 0.07817491, 0.55319383, 0.2176259 ,
              0.09704971, 0.49317679, 0.06315766, 0.08790942, 0.1501398 ,
              0.21665696, 0.23579709, 0.29819007, 0.3497411 , 0.18464204,
              0.1578776 , 0.42834809, 0.09655194, 0.10765619, 0.19653686,
              0.23628055, 0.16701936, 0.29582332, 0.08325537, 0.23609906,
              0.10505704, 0.23114092, 0.14968839, 0.2302336 , 0.2105364 ,
              0.67058982, 0.47292089, 0.24122525, 0.19631579, 0.17362513,
              0.31328028, 0.2562648 , 0.12718644, 0.46851371, 0.24181609,
              0.14474166, 0.30420576, 0.13418311, 0.21842447, 0.2507538 ,
              0.13666702, 0.23586703, 0.58408083, 0.34207287, 0.11223281,
              0.10982336, 0.31975457, 0.22282189, 0.17944722, 0.21874003,
      ...
              0.20688043, 0.47403467, 0.25717756, 0.19066508, 0.12625064,
              0.44768237, 0.16660089, 0.0706952 , 0.16784098, 0.36421198,
              1.46345517, 0.50179268, 0.1523372 , 0.1956238 , 0.14694697,
              0.24004588, 0.11692893, 0.10727995, 1.66596053, 0.18589723,
              0.13322186, 0.13850513, 0.09790181, 0.15698714, 0.16617059,
              0.09406059, 0.10885364, 0.21139588, 0.16196186, 0.16195316,
              0.07182767, 0.31162329, 0.30275279, 0.24104304, 0.12604417,
              0.26921645, 0.27088864, 0.15102642, 0.17063538, 0.41558565,
              0.10870371, 0.16531107, 0.15824463, 0.32388857, 0.14568043,
              0.26336275, 0.13224454, 0.2083225 , 0.04507302, 0.2587414 ,
              0.26198809, 0.07615262, 0.08256953, 0.21247356, 0.21920917,
              0.76939755, 0.20889981, 0.27236234, 0.52139234, 0.14835252,
              0.37085224, 0.3050953 , 0.12233382, 0.11905191, 0.33253917,
              0.14611272, 0.35574692, 0.11257593, 0.18050403, 0.34533744,
              0.22266884, 0.48356926, 0.21836733, 0.1846639 , 0.13248554,
              0.26967546, 0.12959754, 0.25059262, 0.17419057, 0.13497309,
              0.0906121 , 0.12921711, 0.21698366, 0.20942048, 0.04668369,
              0.24006113, 0.064138  , 0.05198891, 0.23646192, 0.53840494,
              0.15887142, 0.12730902, 0.52102642, 0.24299043, 0.14601515,
              0.10681178, 0.18504517, 0.1231525 , 0.24204206, 0.13810632]])

    • z_scale_alpha_New Zealand
      (chain, draw)
      float64
      0.1626 0.2047 ... 0.1554 0.1919

      array([[0.16257979, 0.20473353, 0.1660467 , 0.07499469, 0.36006641,
              0.27578616, 0.33046821, 0.15915183, 0.12910625, 0.13831407,
              0.38751857, 0.0874059 , 0.09957618, 0.48866631, 0.19392543,
              0.16874209, 0.33632883, 0.71572109, 0.13533204, 0.13084356,
              0.17533974, 0.1627762 , 0.41064477, 0.09139926, 0.42826298,
              0.24550348, 0.54457365, 0.109875  , 0.13222741, 0.1482109 ,
              0.15881414, 0.30962614, 0.25116188, 1.26561043, 0.33560544,
              0.33325531, 0.40790865, 0.08030093, 0.44762566, 0.2142664 ,
              0.18684605, 0.15369943, 0.2504877 , 0.15317435, 0.22186467,
              0.09589369, 0.12158797, 0.17326896, 0.04194884, 0.1814088 ,
              0.13621317, 0.30596159, 0.342959  , 0.0943213 , 0.24865241,
              0.10509923, 0.08364646, 0.14001044, 0.10834617, 0.40030199,
              0.09234299, 0.24991498, 0.13387583, 0.21161424, 0.29525061,
              0.78664943, 0.12887164, 0.64957614, 0.19592254, 0.13840067,
              0.13675668, 0.30774641, 0.45503469, 0.72828347, 0.08071809,
              0.27950943, 0.32301921, 0.26599902, 0.15022287, 0.24510993,
              0.27177268, 0.12823048, 0.3827117 , 1.90113199, 0.07435057,
              0.33548514, 0.09668177, 0.18994735, 0.17390371, 0.13445681,
              0.44980731, 0.20885992, 0.20527302, 0.2798389 , 0.44963417,
              0.21717974, 0.09733105, 0.19918713, 0.07762868, 0.13818783,
      ...
              0.25566491, 0.30947523, 0.24619062, 1.89050063, 0.13979159,
              0.11169646, 0.13075423, 0.4799055 , 0.1438906 , 0.10359371,
              0.23691968, 0.20487274, 0.1360907 , 0.19665027, 0.14693158,
              0.45196561, 0.19480535, 0.10585268, 0.32039815, 0.11680072,
              0.43485763, 0.13889767, 0.11705017, 0.08644812, 0.08329165,
              0.18170034, 0.13523083, 0.39954947, 0.22274435, 0.19364089,
              0.22599914, 0.15006166, 0.14756247, 0.28986554, 0.08765432,
              0.08399995, 0.11124613, 0.16629054, 0.27270246, 0.12558614,
              0.08695939, 0.22951728, 0.19615921, 0.11669168, 0.11381599,
              0.71645648, 0.29388051, 0.21441234, 0.18118576, 0.06118888,
              0.2243009 , 0.38444353, 0.16246841, 0.15515467, 0.23542627,
              0.18778183, 0.22342853, 0.35938595, 0.25569006, 0.32454787,
              0.56908536, 0.33990059, 0.11888528, 0.23752101, 0.17677255,
              0.37918781, 0.33519036, 0.09408516, 0.1167565 , 0.10384138,
              0.28937624, 0.14690894, 0.10925158, 0.25924562, 0.09139761,
              0.10794599, 0.15254773, 0.13925995, 0.09375719, 0.15574462,
              0.56007416, 0.64587154, 0.1143188 , 0.32715885, 0.21143106,
              0.1363281 , 0.09308427, 0.09047241, 0.32805184, 0.16646588,
              0.24756532, 0.36085691, 0.14129387, 0.1061752 , 0.12475895,
              0.21138747, 0.24721275, 0.15752091, 0.1553929 , 0.19194603]])

    • noise_chol_United Kingdom_stds
      (chain, draw, noise_chol_United Kingdom_stds_dim_0)
      float64
      0.03717 2.628 ... 0.4055 0.9324

      array([[[3.71684705e-02, 2.62803616e+00, 1.89761851e-03],
              [5.13831503e-01, 9.58806618e-01, 8.79435090e-01],
              [4.04689556e-01, 2.48416636e-01, 2.04990466e-01],
              ...,
              [1.62342154e+00, 9.95776379e-01, 1.13714189e-01],
              [2.92163436e-01, 2.45445126e-01, 5.07074668e-01],
              [2.76772440e+00, 4.05453310e-01, 9.32391346e-01]]])

    • noise_chol_New Zealand_stds
      (chain, draw, noise_chol_New Zealand_stds_dim_0)
      float64
      0.5759 0.01992 ... 0.4947 0.4636

      array([[[0.57589167, 0.01992298, 1.07403478],
              [0.46120014, 0.55327983, 0.07426313],
              [0.42868234, 2.83517613, 1.20754258],
              ...,
              [0.30040541, 0.97758018, 1.67099333],
              [1.10737718, 0.67647755, 2.04557369],
              [0.53009693, 0.49466781, 0.46359907]]])

    • alpha_United States
      (chain, draw, equations)
      float64
      -0.1123 -0.1273 ... -0.1899 -0.2605

      array([[[-0.1122754 , -0.12734704, -0.11031494],
              [ 0.10359595,  0.12226043,  0.0931555 ],
              [ 0.23832381,  0.10872559,  0.21367728],
              ...,
              [ 0.06169654,  0.04741402,  0.12548373],
              [-0.18185839, -0.15345144,  0.44086299],
              [-0.2822267 , -0.18992889, -0.26050735]]])

    • omega_United Kingdom
      (chain, draw, omega_United Kingdom_dim_0, omega_United Kingdom_dim_1)
      float64
      0.9407 0.0 0.0 ... 0.01623 0.9991

      array([[[[ 0.94066212,  0.        ,  0.        ],
               [ 0.52129994,  1.52615182,  0.        ],
               [-0.02478948,  0.02157187,  0.08940098]],
      
              [[ 1.14461231,  0.        ,  0.        ],
               [-0.41585808,  1.1208319 ,  0.        ],
               [-0.80488536, -0.21964174,  0.31724845]],
      
              [[ 0.32303426,  0.        ,  0.        ],
               [-0.02630292,  0.27505622,  0.        ],
               [-0.02302956, -0.13349563,  0.23918957]],
      
              ...,
      
              [[ 1.1429204 ,  0.        ,  0.        ],
               [-0.0091967 ,  0.6614462 ,  0.        ],
               [ 0.02132631, -0.11638239,  0.20265227]],
      
              [[ 0.95053025,  0.        ,  0.        ],
               [-0.35868561,  0.44962075,  0.        ],
               [-0.02624491, -0.0391682 ,  0.42833245]],
      
              [[ 2.61443627,  0.        ,  0.        ],
               [ 1.65874467,  0.38647794,  0.        ],
               [ 0.20439408,  0.01622911,  0.99906375]]]])

    • omega_Australia
      (chain, draw, omega_Australia_dim_0, omega_Australia_dim_1)
      float64
      2.798 0.0 0.0 ... -0.01649 0.6657

      array([[[[ 2.79849438,  0.        ,  0.        ],
               [ 0.05129535,  0.33119208,  0.        ],
               [-0.00809379,  0.18551762,  0.38975745]],
      
              [[ 2.19888565,  0.        ,  0.        ],
               [-0.2283893 ,  1.44020266,  0.        ],
               [-0.74426769, -0.49472631,  0.45332848]],
      
              [[ 0.17032368,  0.        ,  0.        ],
               [ 0.05269687,  0.78212657,  0.        ],
               [ 0.04829656, -0.12379496,  0.29457698]],
      
              ...,
      
              [[ 0.51430996,  0.        ,  0.        ],
               [-0.02749578,  0.10576037,  0.        ],
               [ 0.01963391, -0.10862464,  0.156789  ]],
      
              [[ 1.94167524,  0.        ,  0.        ],
               [-0.25907015,  0.36416895,  0.        ],
               [-0.00998854,  0.13205535,  1.79311081]],
      
              [[ 1.92090981,  0.        ,  0.        ],
               [ 1.64235627,  0.50585178,  0.        ],
               [ 0.31495163, -0.016493  ,  0.66569132]]]])

    • lag_coefs_Australia
      (chain, draw, equations, lags, cross_vars)
      float64
      -0.1962 -0.04238 ... 0.05701 0.0538

      array([[[[[-0.1961536 , -0.04238493, -0.02241971],
                [-0.15077542, -0.21313777, -0.09135567]],
      
               [[-0.19894081, -0.23320756, -0.27911626],
                [ 0.0578797 , -0.30527527, -0.22313689]],
      
               [[-0.22023162,  0.03049929, -0.00585038],
                [-0.1296688 , -0.12040214, -0.09948174]]],
      
      
              [[[-0.22891816, -0.1967858 , -0.21468313],
                [-0.2100601 , -0.24386615, -0.17782713]],
      
               [[-0.25126413, -0.20889774, -0.18437045],
                [-0.20418875, -0.20383443, -0.19456342]],
      
               [[-0.22720345, -0.18963524, -0.2048201 ],
                [-0.2082145 , -0.18245376, -0.1971739 ]]],
      
      
      ...
      
      
              [[[ 0.04336268,  0.03602578,  0.03023212],
                [ 0.04924396, -0.01320222,  0.00612381]],
      
               [[ 0.00549566,  0.01761463, -0.01967821],
                [ 0.03505736,  0.01685139, -0.00436121]],
      
               [[ 0.01222543,  0.02852398,  0.03352444],
                [ 0.01152931, -0.0016901 , -0.01869344]]],
      
      
              [[[ 0.07208268,  0.04829299,  0.07349987],
                [ 0.06538528,  0.05084192,  0.06645425]],
      
               [[ 0.07066286,  0.06578292,  0.06102497],
                [ 0.0391673 ,  0.053377  ,  0.04046732]],
      
               [[ 0.0664287 ,  0.06745102,  0.05934131],
                [ 0.05570972,  0.0570131 ,  0.05380317]]]]])

    • z_scale_beta_New Zealand
      (chain, draw)
      float64
      0.1596 0.3191 ... 0.09559 0.1677

      array([[0.1595764 , 0.31909431, 0.14984458, 0.473567  , 0.30314647,
              0.41680411, 0.14055266, 0.21443999, 0.28680193, 0.207827  ,
              0.12470213, 0.27358584, 0.15877701, 0.1766966 , 0.31672804,
              0.34511963, 0.20636382, 0.17567789, 0.37350301, 0.16425487,
              0.44202529, 0.17671469, 1.0025769 , 0.17129725, 0.11397575,
              0.36668509, 0.12703921, 0.31440648, 0.65616426, 0.27927965,
              0.07146724, 0.29072444, 0.30097163, 0.42272131, 0.50763782,
              0.11535842, 0.19219011, 0.08155474, 0.14333571, 0.10171381,
              0.16189723, 0.09084773, 0.18996573, 0.28882752, 0.5236453 ,
              0.6868979 , 0.26741783, 0.08599283, 0.13714952, 0.32331594,
              0.85861371, 0.13800996, 0.56831276, 0.15072784, 0.14006245,
              0.18924386, 0.16490975, 0.2730547 , 1.81338977, 0.21590061,
              0.13114485, 0.19547382, 0.30880499, 0.11408552, 0.18137243,
              0.48850668, 0.35926686, 0.11678598, 0.18221083, 0.0764939 ,
              0.59665507, 0.16989122, 0.10456052, 0.28523524, 0.52829938,
              0.63250685, 0.11275178, 0.47830736, 0.20330458, 0.05676593,
              0.22213268, 0.37820405, 0.11673709, 0.15349803, 0.13847562,
              0.45858207, 0.28596827, 0.09620013, 0.09036497, 0.06405045,
              0.20398546, 0.19810778, 0.09165543, 0.15941918, 0.28383069,
              0.16264909, 0.24714102, 0.41887418, 0.11412962, 0.22608534,
      ...
              0.09466267, 0.32698251, 0.24179005, 0.17866664, 0.14031657,
              0.14328991, 0.18572951, 0.18990388, 0.23515911, 0.45604518,
              0.05824148, 0.16369792, 0.0536564 , 0.14770094, 0.49495615,
              0.10217579, 0.11772349, 0.07809962, 0.14428259, 0.17064257,
              0.13764948, 0.18450781, 0.17910942, 0.24048955, 0.13946675,
              0.21332236, 0.08934233, 0.12498345, 0.08966867, 0.24637675,
              0.1822877 , 0.19826166, 0.11381018, 0.25234185, 0.1336435 ,
              0.09102639, 0.92209292, 0.27710708, 0.24156467, 0.13801857,
              0.36776389, 0.15985224, 0.44076973, 0.14350409, 0.19963751,
              0.70209226, 0.18562798, 0.19088137, 0.10218107, 0.19664039,
              0.10636086, 0.24755424, 0.25374839, 0.06738148, 0.21254131,
              0.56908049, 0.34745447, 0.44286962, 0.21850306, 0.21384828,
              0.1672484 , 0.34116064, 0.16123007, 0.10147714, 0.61500581,
              0.17133974, 0.60976176, 0.12176558, 0.16685053, 0.06602818,
              0.18366747, 0.14912495, 0.14119082, 0.22471715, 0.25352004,
              0.63217796, 0.38316989, 0.77526843, 0.14541542, 0.12339019,
              0.0495911 , 0.28415788, 0.184606  , 0.59120927, 0.13984808,
              0.42151482, 0.54217349, 0.1484539 , 0.11815923, 0.11127211,
              0.29087105, 0.13832078, 0.2819072 , 0.13687175, 0.49502223,
              0.18897839, 0.07491648, 0.06200944, 0.09559076, 0.16772793]])

    • alpha_New Zealand
      (chain, draw, equations)
      float64
      -0.1341 -0.1184 ... -0.309 -0.2621

      array([[[-0.13411454, -0.11837157, -0.09823672],
              [ 0.06188021,  0.03255268,  0.06646392],
              [ 0.20641065,  0.1379772 ,  0.19274663],
              ...,
              [ 0.09546404,  0.06121229,  0.03803407],
              [ 0.05411883,  0.02830194,  0.05475787],
              [-0.26640311, -0.30904358, -0.26214372]]])

    • lag_coefs_Ireland
      (chain, draw, equations, lags, cross_vars)
      float64
      -0.1868 -0.1527 ... 0.06407 0.05551

      array([[[[[-0.18678705, -0.15265051, -0.14907884],
                [-0.18391385, -0.18808559, -0.12134384]],
      
               [[-0.19569234, -0.24607583, -0.17957038],
                [-0.16946666, -0.14072849, -0.21832593]],
      
               [[-0.17528042, -0.21988379, -0.17378612],
                [-0.19794297, -0.15543846, -0.12668154]]],
      
      
              [[[-0.20297659, -0.19835389, -0.22150673],
                [-0.21533709, -0.21462178, -0.21762576]],
      
               [[-0.22332784, -0.20240641, -0.21523745],
                [-0.1852436 , -0.21375762, -0.19681   ]],
      
               [[-0.20094811, -0.201738  , -0.2196669 ],
                [-0.18584382, -0.19476701, -0.19170025]]],
      
      
      ...
      
      
              [[[ 0.17158737,  0.17518965,  0.05365764],
                [-0.01095842,  0.06114475,  0.02548319]],
      
               [[-0.0470689 ,  0.08979091,  0.04993573],
                [ 0.05302195, -0.01399206,  0.05093116]],
      
               [[-0.07491731,  0.07711348,  0.02723354],
                [ 0.07700294, -0.00584274,  0.07558744]]],
      
      
              [[[ 0.06073059,  0.05678287,  0.0623281 ],
                [ 0.05840248,  0.05519933,  0.06312752]],
      
               [[ 0.05587671,  0.06360262,  0.05175008],
                [ 0.06448157,  0.04623022,  0.06312355]],
      
               [[ 0.05817472,  0.06320071,  0.04800966],
                [ 0.06643841,  0.06407291,  0.05550688]]]]])

    • noise_chol_South Africa_stds
      (chain, draw, noise_chol_South Africa_stds_dim_0)
      float64
      1.581 1.826 ... 0.3287 0.1919

      array([[[1.5812284 , 1.82584772, 0.0377774 ],
              [3.29713432, 0.3247918 , 2.89313015],
              [0.87096432, 0.68098054, 1.80229825],
              ...,
              [0.66252934, 1.86436534, 2.17409475],
              [0.28618202, 0.74769883, 0.5660671 ],
              [0.16104663, 0.32867603, 0.19188381]]])

    • alpha_South Africa
      (chain, draw, equations)
      float64
      -0.1202 -0.1137 ... -0.2432 -0.2544

      array([[[-0.12022232, -0.11367182, -0.10794469],
              [ 0.07282995,  0.04322713,  0.06724012],
              [ 0.06996945,  0.14752209,  0.16313593],
              ...,
              [ 0.11707275,  0.05555555, -0.16032398],
              [ 0.04373721,  0.09431552,  0.04430106],
              [-0.26879254, -0.24317041, -0.25442029]]])

    • omega_Ireland
      (chain, draw, omega_Ireland_dim_0, omega_Ireland_dim_1)
      float64
      2.586 0.0 0.0 ... 0.0008263 0.8505

      array([[[[ 2.58639628e+00,  0.00000000e+00,  0.00000000e+00],
               [ 4.09927426e-01,  1.35269659e+00,  0.00000000e+00],
               [-5.37619633e-02,  2.44418105e-02,  1.83495101e-01]],
      
              [[ 1.18559436e+00,  0.00000000e+00,  0.00000000e+00],
               [-4.93503902e-01,  1.07422866e+00,  0.00000000e+00],
               [-7.72675644e-01, -3.98223351e-01,  1.55929365e-01]],
      
              [[ 5.19799071e-01,  0.00000000e+00,  0.00000000e+00],
               [ 3.33304174e-02,  1.56625045e+00,  0.00000000e+00],
               [-8.12668016e-02, -7.65072574e-02,  4.02325125e-01]],
      
              ...,
      
              [[ 9.03289140e-01,  0.00000000e+00,  0.00000000e+00],
               [-8.16329007e-02,  7.61894507e-01,  0.00000000e+00],
               [ 2.95952632e-01, -3.81254889e-01,  1.64034000e+00]],
      
              [[ 1.99897232e+00,  0.00000000e+00,  0.00000000e+00],
               [-2.06124180e-01,  7.66606308e-01,  0.00000000e+00],
               [-1.73635520e-02,  1.48188438e-01,  8.50744813e-01]],
      
              [[ 1.95106390e+00,  0.00000000e+00,  0.00000000e+00],
               [ 1.74963152e+00,  4.01199909e-01,  0.00000000e+00],
               [ 3.53497383e-01,  8.26304021e-04,  8.50474997e-01]]]])

    • lag_coefs_United Kingdom
      (chain, draw, equations, lags, cross_vars)
      float64
      -0.3605 -0.1986 ... 0.06297 0.06245

      array([[[[[-0.36052092, -0.19860953,  0.02177938],
                [-0.03464429, -0.09187011, -0.43320885]],
      
               [[ 0.03266122,  0.05491349, -0.33003956],
                [-0.24663718, -0.32606953, -0.15747561]],
      
               [[-0.0260827 , -0.12671588, -0.25819839],
                [ 0.00386647,  0.06725576, -0.38870329]]],
      
      
              [[[-0.26505344, -0.20221769, -0.2292391 ],
                [-0.19091368, -0.24630777, -0.16210045]],
      
               [[-0.15381381, -0.24810409, -0.16861722],
                [-0.14581489, -0.19537078, -0.19954608]],
      
               [[-0.22349155, -0.19670298, -0.18637268],
                [-0.14958251, -0.14433438, -0.2048611 ]]],
      
      
      ...
      
      
              [[[ 0.0037063 ,  0.07384256,  0.0575044 ],
                [-0.04287917,  0.07976311, -0.00292942]],
      
               [[ 0.04505964, -0.00613842,  0.08048952],
                [-0.01867705,  0.01364884, -0.078449  ]],
      
               [[-0.0179588 ,  0.02668368, -0.02074897],
                [ 0.04733557, -0.04998428, -0.04249807]]],
      
      
              [[[ 0.06611016,  0.04871902,  0.05118372],
                [ 0.0757195 ,  0.05552676,  0.06288292]],
      
               [[ 0.0604792 ,  0.06258736,  0.05946574],
                [ 0.06521125,  0.0639017 ,  0.06616612]],
      
               [[ 0.04742713,  0.07416921,  0.04645026],
                [ 0.05075313,  0.06297496,  0.06244988]]]]])

    • alpha_Canada
      (chain, draw, equations)
      float64
      -0.1172 -0.1188 ... -0.2555 -0.2642

      array([[[-0.11724578, -0.11883244, -0.11291433],
              [ 0.05042853,  0.05767736,  0.10802469],
              [ 0.21811029,  0.23366782,  0.20019744],
              ...,
              [ 0.13969839,  0.04808045,  0.10640985],
              [ 0.06852303,  0.07106682,  0.06308139],
              [-0.23532934, -0.25552875, -0.26415459]]])

    • z_scale_beta_Ireland
      (chain, draw)
      float64
      0.07163 0.08413 ... 0.3716 0.1233

      array([[0.07163329, 0.08413478, 0.08755404, 0.23453179, 0.30542108,
              0.43203706, 0.11621525, 0.22725081, 0.14066017, 0.06447647,
              0.18195441, 0.2979855 , 0.25577131, 0.07385324, 0.14376264,
              0.12304787, 0.83388509, 0.11786395, 0.17542277, 0.13408145,
              0.27892992, 0.11153842, 0.13897429, 0.14334591, 0.13401484,
              0.14252127, 0.39030187, 0.15815744, 0.07312245, 0.13120768,
              0.22964085, 0.19894006, 0.10616301, 0.15233651, 0.45655982,
              0.1301663 , 0.972213  , 0.24668618, 0.22498558, 0.22384238,
              0.19722808, 0.21387158, 0.34359696, 0.07736254, 0.14463155,
              1.0583714 , 0.12364719, 0.16719231, 0.10613701, 0.13767955,
              0.23892066, 0.17893978, 0.33054068, 0.12373109, 0.18793181,
              0.82859709, 0.45311229, 0.18805356, 0.1728399 , 0.15028426,
              0.25672119, 0.18429149, 0.24616073, 0.19184509, 0.11043875,
              0.21774424, 0.18178512, 0.17160492, 0.14600922, 0.32059958,
              0.19876657, 0.4457766 , 1.14460319, 0.31732579, 0.29761875,
              0.05390961, 0.12838263, 0.26261061, 1.29202241, 0.13479564,
              0.18347114, 0.14445945, 0.11380765, 0.23588144, 0.28325807,
              0.06268906, 0.24010887, 0.08551197, 0.14933643, 0.31853377,
              0.28051309, 0.13742563, 0.17363697, 0.17822277, 0.12570658,
              0.22254829, 0.11654764, 0.31638426, 0.1752214 , 0.06424156,
      ...
              0.18017406, 0.25107532, 0.14125656, 0.1340293 , 0.15143401,
              0.17979784, 0.10230655, 0.09610106, 0.23308408, 0.16685291,
              0.35500314, 0.11487525, 0.14464978, 0.42393198, 0.91474375,
              0.11772092, 0.51607064, 0.13537261, 0.11358025, 0.11583106,
              0.19417048, 0.13565478, 0.23522559, 0.0905361 , 0.10013519,
              0.19108106, 0.16220839, 0.32430115, 0.07865016, 0.28852676,
              0.18530219, 0.26364345, 0.05486286, 0.29282799, 0.10392355,
              0.49220611, 0.15431847, 0.08114926, 0.46771052, 0.27909326,
              0.21189142, 0.11080887, 0.49201439, 0.20806369, 0.3919624 ,
              0.29717214, 0.08647545, 0.1629127 , 0.11928048, 0.10979854,
              0.1155407 , 0.29554581, 0.16796259, 0.77389029, 0.16345719,
              0.35637281, 0.09542406, 0.39445065, 0.23896037, 0.13337993,
              0.13671295, 0.06786871, 0.15321679, 0.64859899, 0.1688205 ,
              0.16550456, 0.28892148, 1.02925402, 0.12911254, 0.44169065,
              1.09725051, 0.12139197, 0.15877436, 0.53522059, 0.25541761,
              2.50454558, 0.16618171, 0.54993892, 0.29564516, 0.12609919,
              0.1834574 , 0.61799822, 0.10576515, 0.53324708, 1.50356317,
              0.26191044, 0.41923726, 0.08723944, 0.30142969, 0.06410624,
              0.20717064, 0.08829394, 0.10641084, 0.65765017, 0.42985316,
              0.08507945, 0.24317143, 0.16548908, 0.37164655, 0.12326749]])

    • noise_chol_Chile_corr
      (chain, draw, noise_chol_Chile_corr_dim_0, noise_chol_Chile_corr_dim_1)
      float64
      1.0 -0.1709 0.1487 ... -0.3751 1.0

      array([[[[ 1.        , -0.17090528,  0.14869546],
               [-0.17090528,  1.        ,  0.21319977],
               [ 0.14869546,  0.21319977,  1.        ]],
      
              [[ 1.        , -0.39296326,  0.24200419],
               [-0.39296326,  1.        , -0.07165122],
               [ 0.24200419, -0.07165122,  1.        ]],
      
              [[ 1.        , -0.03235085,  0.37344916],
               [-0.03235085,  1.        ,  0.03250628],
               [ 0.37344916,  0.03250628,  1.        ]],
      
              ...,
      
              [[ 1.        , -0.25233108, -0.34355138],
               [-0.25233108,  1.        ,  0.07825342],
               [-0.34355138,  0.07825342,  1.        ]],
      
              [[ 1.        ,  0.30324589,  0.23548559],
               [ 0.30324589,  1.        ,  0.29728758],
               [ 0.23548559,  0.29728758,  1.        ]],
      
              [[ 1.        , -0.27067426,  0.05400277],
               [-0.27067426,  1.        , -0.37509298],
               [ 0.05400277, -0.37509298,  1.        ]]]])

    • noise_chol_United States_stds
      (chain, draw, noise_chol_United States_stds_dim_0)
      float64
      1.025 2.018 0.5789 ... 0.619 0.2143

      array([[[1.02485906, 2.01769132, 0.57885858],
              [0.12223676, 0.34959891, 0.81983802],
              [1.81531772, 1.2366803 , 2.8199029 ],
              ...,
              [0.63896902, 0.23374696, 3.08903391],
              [0.93403749, 1.1745727 , 0.23355354],
              [0.91164171, 0.61897674, 0.21429496]]])

    • omega_United States
      (chain, draw, omega_United States_dim_0, omega_United States_dim_1)
      float64
      1.48 0.0 0.0 ... -0.002397 0.7022

      array([[[[ 1.4798585 ,  0.        ,  0.        ],
               [ 0.07280083,  1.27139482,  0.        ],
               [-0.0490548 ,  0.15088609,  0.3760185 ]],
      
              [[ 1.02459204,  0.        ,  0.        ],
               [-0.49268994,  0.94289404,  0.        ],
               [-0.73130831, -0.31803447,  0.34975097]],
      
              [[ 1.23923872,  0.        ,  0.        ],
               [-0.10186104,  0.92091395,  0.        ],
               [ 0.07675077,  0.7677725 ,  1.71391872]],
      
              ...,
      
              [[ 0.57856465,  0.        ,  0.        ],
               [-0.02838119,  0.22482083,  0.        ],
               [-0.66458456, -0.06387396,  1.77003816]],
      
              [[ 1.47939746,  0.        ,  0.        ],
               [-0.32124116,  1.23342166,  0.        ],
               [-0.02755179, -0.00738831,  0.20319158]],
      
              [[ 1.82199953,  0.        ,  0.        ],
               [ 1.80787964,  0.46908523,  0.        ],
               [ 0.28886718, -0.00239748,  0.70220697]]]])

    • lag_coefs_New Zealand
      (chain, draw, equations, lags, cross_vars)
      float64
      -0.2065 -0.1456 ... 0.06747 0.05084

      array([[[[[-0.20654316, -0.14562934, -0.26288777],
                [-0.16641344, -0.15950696, -0.11481519]],
      
               [[-0.25234332, -0.10828001, -0.192556  ],
                [-0.13940197, -0.2283368 , -0.12041435]],
      
               [[-0.1208677 , -0.23817163, -0.19558745],
                [-0.13492058, -0.06619099, -0.21045424]]],
      
      
              [[[-0.32770078, -0.10647709, -0.2173961 ],
                [-0.11299811, -0.09182672, -0.25010002]],
      
               [[-0.15915056, -0.28384819, -0.15889862],
                [-0.10944911, -0.20428178, -0.22873497]],
      
               [[-0.18243547, -0.21476259, -0.08634329],
                [-0.19036886, -0.1796177 , -0.19128967]]],
      
      
      ...
      
      
              [[[ 0.02159585,  0.03169854,  0.02494288],
                [ 0.01473301,  0.02966987, -0.01652773]],
      
               [[ 0.01446537, -0.00331149,  0.00869062],
                [ 0.00396315, -0.01732477,  0.01578873]],
      
               [[ 0.03041103,  0.01238237,  0.01386057],
                [ 0.00996718,  0.07574674,  0.02485907]]],
      
      
              [[[ 0.04620779,  0.05968816,  0.06256686],
                [ 0.04269093,  0.059605  ,  0.05580936]],
      
               [[ 0.05003254,  0.06448281,  0.06014105],
                [ 0.06150055,  0.05707461,  0.06059594]],
      
               [[ 0.05997411,  0.0561341 ,  0.05838696],
                [ 0.06310736,  0.06746523,  0.05083574]]]]])

    • z_scale_beta_Australia
      (chain, draw)
      float64
      0.2788 0.1047 ... 0.08373 0.2213

      array([[0.27881565, 0.10469813, 0.1211257 , 0.25124204, 0.16018028,
              0.23515602, 0.16096252, 0.29431363, 0.98003321, 0.15331914,
              0.09585257, 0.09113346, 0.0837121 , 0.1312792 , 0.88342217,
              0.164084  , 0.44128772, 0.37055024, 0.07643875, 0.24940322,
              0.2673004 , 0.18368429, 0.33493299, 0.1157403 , 0.1971344 ,
              0.60712343, 0.1726061 , 0.16856774, 0.09592041, 0.12013222,
              0.1370233 , 0.2426129 , 0.30202182, 0.28234465, 0.71192041,
              0.05518795, 0.21404515, 0.14405558, 0.155575  , 0.26943012,
              0.28554819, 0.09805847, 0.09992052, 0.19794793, 0.31936183,
              0.10023596, 0.07385885, 0.26026719, 0.25966287, 0.15740078,
              0.28298877, 0.23618574, 0.10719332, 0.18815603, 0.19847085,
              0.09465452, 0.13741752, 0.14836489, 0.25264099, 0.41073982,
              0.08606129, 0.12396397, 0.31378118, 0.12070497, 0.51071   ,
              0.23677943, 0.18116091, 0.20819466, 0.17827292, 0.17258466,
              0.15612765, 0.12282135, 0.18750847, 0.14498828, 0.10212388,
              0.19377678, 0.31166066, 0.10249523, 0.27172758, 0.42374111,
              1.27183713, 0.21220824, 0.18636243, 0.31130914, 0.10902415,
              0.10676085, 0.12933155, 0.35427775, 0.25906178, 0.53339082,
              0.22363702, 0.34051648, 0.15133265, 0.13279198, 0.14951954,
              0.14884373, 0.44572052, 0.20747406, 0.24888566, 0.1628897 ,
      ...
              0.10074804, 0.24566984, 0.14527515, 0.21195912, 0.29674904,
              0.39399415, 0.24526314, 0.16635332, 0.12266914, 0.11014299,
              0.11756377, 0.19903654, 0.13099525, 0.20033183, 0.1225756 ,
              0.15833845, 0.07301871, 0.10099471, 0.26370506, 0.09525833,
              0.25715513, 0.22447191, 0.7251473 , 0.24861478, 0.06885664,
              0.11701662, 0.4595473 , 0.8219404 , 0.19257692, 0.34735225,
              0.18519346, 0.1219051 , 0.28037848, 0.23374819, 0.18555476,
              0.20611156, 0.20997989, 0.13054928, 0.41153894, 0.29190641,
              0.32473762, 0.09319944, 0.22788271, 0.11747517, 0.08590645,
              0.35781655, 0.10869864, 0.26159247, 0.205304  , 0.32638852,
              0.15692531, 0.3650207 , 0.16708497, 0.1859105 , 0.09055496,
              0.18565301, 0.28684467, 0.12816474, 0.2203393 , 0.28199904,
              0.26975798, 0.15679835, 0.07407453, 0.16824704, 0.3836013 ,
              0.05707429, 0.20832219, 0.10882047, 0.94681812, 0.10141334,
              0.17883141, 0.42572401, 0.15002428, 0.2590692 , 0.125405  ,
              0.1197349 , 0.41379128, 0.47283222, 0.22757644, 0.2949491 ,
              0.17909723, 0.34026183, 0.17221909, 0.11406275, 0.17099736,
              0.32597273, 0.16747589, 0.09508129, 0.65332027, 0.13359989,
              0.47814597, 0.07304196, 0.08927572, 0.15589993, 0.23143155,
              0.28141908, 0.19219578, 0.11351882, 0.08373141, 0.22127545]])

    • noise_chol_New Zealand
      (chain, draw, noise_chol_New Zealand_dim_0)
      float64
      0.5759 0.007675 ... -0.04572 0.4611

      array([[[ 0.57589167,  0.0076753 ,  0.01838518,  0.27958843,
               -0.31350159,  0.98848256],
              [ 0.46120014,  0.08143382,  0.54725415, -0.05300044,
                0.00530818,  0.05174736],
              [ 0.42868234,  0.10437683,  2.83325416,  0.05997802,
               -0.36911415,  1.14817963],
              ...,
              [ 0.30040541, -0.2104437 ,  0.95466039, -0.64734286,
                0.09880133,  1.53733673],
              [ 1.10737718,  0.05896507,  0.67390281,  0.56472082,
               -0.37005175,  1.93093858],
              [ 0.53009693, -0.03661856,  0.49331058,  0.01351801,
               -0.04571649,  0.46114137]]])

    • omega_Chile
      (chain, draw, omega_Chile_dim_0, omega_Chile_dim_1)
      float64
      0.936 0.0 0.0 ... -0.09397 0.7722

      array([[[[ 9.36020417e-01,  0.00000000e+00,  0.00000000e+00],
               [ 1.52401959e-02,  3.87128043e-01,  0.00000000e+00],
               [ 4.37408784e-02,  1.33147881e-01,  5.28437735e-01]],
      
              [[ 1.04733738e+00,  0.00000000e+00,  0.00000000e+00],
               [-5.38931203e-01,  9.55919656e-01,  0.00000000e+00],
               [-7.35513836e-01, -3.86820347e-01,  2.41585067e-01]],
      
              [[ 3.26869831e+00,  0.00000000e+00,  0.00000000e+00],
               [ 3.30205840e-02,  5.90436206e-01,  0.00000000e+00],
               [ 5.97951794e-01, -4.83281138e-02,  1.56179601e+00]],
      
              ...,
      
              [[ 2.14014411e-01,  0.00000000e+00,  0.00000000e+00],
               [-5.36481580e-01,  2.04876587e+00,  0.00000000e+00],
               [-2.37240883e-02, -1.15618572e-01,  2.56096869e-01]],
      
              [[ 8.57876950e-01,  0.00000000e+00,  0.00000000e+00],
               [ 8.80571205e-04,  1.12448908e+00,  0.00000000e+00],
               [ 2.98983373e-01,  3.01371030e-01,  1.27409569e+00]],
      
              [[ 1.56441016e+00,  0.00000000e+00,  0.00000000e+00],
               [ 1.52603411e+00,  8.88917038e-01,  0.00000000e+00],
               [ 3.23267111e-01, -9.39733478e-02,  7.72182687e-01]]]])

    • z_scale_alpha_Australia
      (chain, draw)
      float64
      0.2135 0.558 ... 0.1505 0.283

      array([[0.21349685, 0.55798781, 0.89276486, 0.0929538 , 0.16229627,
              0.12217945, 0.19102479, 0.12181753, 0.26815972, 0.12455234,
              0.14814762, 0.13467901, 0.31316463, 0.38224019, 0.09268671,
              0.28875773, 0.17290106, 0.08494782, 0.16675921, 0.18716972,
              0.0906609 , 0.39631931, 0.13631636, 0.12975208, 0.18477318,
              0.13932279, 0.10940528, 1.07689583, 0.11714862, 0.35288666,
              0.46205462, 0.17280418, 0.15916952, 0.08627822, 0.39790241,
              0.16470455, 0.34617587, 0.29920837, 0.45214034, 0.25277276,
              0.31529658, 0.0796127 , 0.12027817, 0.2970992 , 0.18230463,
              0.30367395, 0.10165875, 0.25707323, 0.34925061, 0.13220736,
              0.13025155, 0.17074058, 0.09000912, 0.32023614, 0.0934971 ,
              0.15784082, 0.25430052, 0.32815974, 0.16281204, 0.16189498,
              0.0796007 , 0.20408872, 0.15960882, 0.19821208, 0.10822714,
              0.31919547, 0.4725085 , 0.1297642 , 0.13783116, 0.16311501,
              0.07950005, 0.16803838, 0.22591461, 0.1850961 , 0.41528212,
              0.23679564, 0.27401552, 0.13444167, 0.22487896, 0.10652259,
              0.12493599, 0.21251467, 0.15683186, 0.11963954, 0.24229907,
              0.18876937, 0.19871174, 0.1161395 , 0.16222612, 0.17238744,
              0.25550942, 0.23321398, 0.11471119, 0.15866093, 0.18912152,
              0.268599  , 0.20141053, 0.23590482, 0.11265815, 0.16831428,
      ...
              0.32098438, 0.33982917, 0.15818539, 0.1181535 , 0.13422332,
              0.10383103, 0.15148347, 0.27367008, 0.37663366, 0.65801811,
              0.22779821, 0.12107004, 0.14691564, 0.1583824 , 0.13815032,
              0.29145257, 0.1324747 , 0.71650209, 0.08977658, 0.25536085,
              0.23384534, 0.24988145, 0.11220109, 0.51525044, 0.16830479,
              0.1459533 , 0.25387926, 0.61865403, 2.39769012, 0.14074619,
              0.38246219, 0.19007745, 0.10237864, 0.08020918, 0.2269304 ,
              0.15385598, 0.1881944 , 0.12722658, 0.68554785, 0.29884224,
              0.26259276, 0.29588416, 0.08275737, 0.4399304 , 0.21779385,
              0.66440144, 0.08841264, 0.21978646, 0.18137905, 0.11109064,
              0.53287206, 0.07603271, 0.24072975, 0.35999341, 0.23792117,
              0.22200911, 0.12065137, 0.13772612, 0.21153311, 0.38971295,
              0.07261891, 0.2049971 , 0.25216086, 0.32072983, 0.29977723,
              0.46945961, 0.22070712, 0.49405479, 0.21245975, 0.8270608 ,
              0.09507272, 0.13288111, 0.16609586, 0.1783188 , 0.20623537,
              0.23260991, 0.26462791, 0.71120718, 0.12302289, 0.19987558,
              0.12040077, 0.15655036, 0.1692955 , 0.11366119, 0.07819533,
              0.09425215, 0.16759718, 0.30319109, 0.2926074 , 0.09344479,
              0.16946023, 0.24534464, 0.17671518, 0.26588803, 0.26731759,
              0.06168833, 0.11848901, 0.12463534, 0.15053058, 0.28295018]])

    • noise_chol_United States
      (chain, draw, noise_chol_United States_dim_0)
      float64
      1.025 0.03648 ... 0.06989 0.1936

      array([[[ 1.02485906,  0.03647595,  2.01736158, -0.0450058 ,
                0.23603656,  0.52662935],
              [ 0.12223676, -0.01651957,  0.3492084 ,  0.11932015,
                0.23555674,  0.77615083],
              [ 1.81531772, -0.2305273 ,  1.21500425,  0.09710938,
                1.36396402,  2.46617604],
              ...,
              [ 0.63896902, -0.00430105,  0.23370739, -1.19358163,
                0.08834221,  2.84775158],
              [ 0.93403749, -0.05972324,  1.17305335, -0.01338253,
                0.01071785,  0.23292336],
              [ 0.91164171,  0.22110833,  0.5781378 , -0.05971827,
                0.06988621,  0.19357679]]])

    • lag_coefs_South Africa
      (chain, draw, equations, lags, cross_vars)
      float64
      -0.2365 -0.1754 ... 0.05666 0.05853

      array([[[[[-0.23653396, -0.17535764, -0.19259883],
                [-0.23701861, -0.10574879, -0.19480722]],
      
               [[-0.19592983, -0.12407823, -0.17365097],
                [-0.15210075, -0.07545554, -0.21088623]],
      
               [[-0.25404572, -0.21689502, -0.16918229],
                [-0.12288923, -0.14146429, -0.19812718]]],
      
      
              [[[-0.25672551, -0.22618817, -0.18411549],
                [-0.24591878, -0.27018902, -0.27187515]],
      
               [[-0.22940812, -0.1967032 , -0.19118466],
                [-0.23785843, -0.18149571, -0.20791851]],
      
               [[-0.18135597, -0.17611271, -0.28292983],
                [-0.20437799, -0.1659736 , -0.24030227]]],
      
      
      ...
      
      
              [[[ 0.00319377,  0.03971881,  0.04003112],
                [ 0.07366218, -0.03378931,  0.14260651]],
      
               [[-0.03996608, -0.00224961, -0.03843742],
                [ 0.01421821, -0.01586986, -0.05962431]],
      
               [[ 0.00375386,  0.1397171 ,  0.09193438],
                [-0.06978229, -0.10550759, -0.09893312]]],
      
      
              [[[ 0.03846222,  0.06165028,  0.0582391 ],
                [ 0.04459164,  0.05316985,  0.05482073]],
      
               [[ 0.0377817 ,  0.06268424,  0.08046469],
                [ 0.04958416,  0.05165488,  0.06246147]],
      
               [[ 0.03785436,  0.05958385,  0.05252461],
                [ 0.05541533,  0.05665948,  0.05853228]]]]])

    • z_scale_beta_Canada
      (chain, draw)
      float64
      0.206 0.1572 0.062 ... 0.2 0.1907

      array([[0.20597835, 0.15715561, 0.062     , 0.21010669, 0.28258379,
              0.11517814, 0.30118359, 0.48763144, 0.37490842, 0.08627406,
              0.08519334, 0.11332028, 0.27016606, 0.1155351 , 0.12088698,
              0.43648722, 0.24707822, 0.12911647, 0.18902934, 0.15183204,
              0.32300672, 0.2541712 , 0.15232288, 0.20628871, 0.32135944,
              0.21188144, 0.10275504, 0.20189652, 0.11160093, 0.16513119,
              0.27321642, 0.17276446, 0.590317  , 0.21623107, 0.16032405,
              0.1484018 , 0.23818659, 0.15288073, 0.16149012, 0.12235722,
              0.09850244, 0.12354564, 0.13699863, 0.35075085, 0.67227034,
              0.31109322, 0.06269607, 0.26313699, 0.44222567, 0.31281536,
              0.64379277, 0.09593582, 0.16328929, 0.6698961 , 0.12044611,
              0.26743635, 0.22373021, 0.67184493, 0.07137944, 0.48541162,
              0.31137895, 0.13695403, 0.19946058, 0.21471459, 0.2345619 ,
              0.19579824, 0.12624404, 0.18195879, 0.2321122 , 0.18688321,
              0.17116901, 0.42275027, 0.22626851, 0.08654082, 0.21525921,
              0.06693556, 0.20763649, 0.18333726, 0.5773455 , 0.08616333,
              0.37190231, 0.20615889, 0.52651009, 0.19026844, 0.08872785,
              0.12709443, 0.13739737, 0.29774602, 0.19083827, 0.08953584,
              0.24023509, 0.18150133, 0.1622077 , 0.10278121, 0.28490485,
              0.79936355, 0.10746417, 0.72094253, 0.13005678, 0.1692404 ,
      ...
              0.12591114, 0.09727694, 0.12564752, 0.13456127, 0.14667568,
              0.37183583, 0.11748543, 0.15256233, 0.45761602, 0.19443811,
              0.42583561, 0.50855639, 0.53799702, 0.18945073, 0.94775416,
              0.22755719, 0.15736608, 0.19850553, 0.20375117, 0.29020824,
              0.24507071, 0.13249971, 0.68559728, 0.12291209, 0.14090839,
              0.0674714 , 0.62049209, 0.42207586, 0.1717535 , 0.13568536,
              0.09318577, 0.08745766, 0.18766408, 0.25468481, 0.1937421 ,
              0.1074329 , 0.39462298, 0.17551673, 0.14620555, 0.09398065,
              0.21262622, 0.32647654, 0.13420811, 0.18585891, 0.49753251,
              0.15809565, 0.05227775, 0.1335445 , 0.13660069, 0.27004503,
              0.15732034, 0.36840803, 0.15603986, 0.34394718, 0.08431872,
              0.27838542, 0.71138281, 0.5397544 , 0.23548402, 0.22775199,
              0.14072805, 0.85468932, 0.08632006, 0.13319566, 0.16904253,
              0.16330327, 0.11303598, 0.14150272, 0.19259192, 0.39271348,
              0.20441471, 0.20754252, 0.21929124, 0.8280654 , 0.17102702,
              0.10245022, 0.16402004, 0.17161117, 0.33091494, 0.16519594,
              0.60766513, 0.06786667, 0.16778956, 0.39310014, 0.21843639,
              0.10776247, 0.09070453, 0.65914102, 0.11487672, 0.19322548,
              0.12971926, 0.11234246, 0.75772232, 0.24139028, 0.08129723,
              0.09606349, 0.24675547, 0.1075058 , 0.20003389, 0.19066278]])

    • noise_chol_United Kingdom_corr
      (chain, draw, noise_chol_United Kingdom_corr_dim_0, noise_chol_United Kingdom_corr_dim_1)
      float64
      1.0 0.3265 -0.2935 ... 0.2028 1.0

      array([[[[ 1.        ,  0.3264905 , -0.29353167],
               [ 0.3264905 ,  1.        , -0.51373321],
               [-0.29353167, -0.51373321,  1.        ]],
      
              [[ 1.        ,  0.24422305, -0.13729554],
               [ 0.24422305,  1.        ,  0.58019564],
               [-0.13729554,  0.58019564,  1.        ]],
      
              [[ 1.        , -0.45969038, -0.27570427],
               [-0.45969038,  1.        ,  0.02420394],
               [-0.27570427,  0.02420394,  1.        ]],
      
              ...,
      
              [[ 1.        ,  0.02928775,  0.02558654],
               [ 0.02928775,  1.        , -0.02784166],
               [ 0.02558654, -0.02784166,  1.        ]],
      
              [[ 1.        , -0.42848156, -0.02326362],
               [-0.42848156,  1.        , -0.03966232],
               [-0.02326362, -0.03966232,  1.        ]],
      
              [[ 1.        , -0.31619581, -0.27625219],
               [-0.31619581,  1.        ,  0.20284884],
               [-0.27625219,  0.20284884,  1.        ]]]])

    • betaX_United Kingdom
      (chain, draw, betaX_United Kingdom_dim_0, betaX_United Kingdom_dim_1)
      float64
      -0.03942 -0.0173 ... -0.01429

      array([[[[-3.94200727e-02, -1.72960150e-02, -1.37328921e-02],
               [-3.79317591e-02, -4.53373613e-02, -2.01338350e-02],
               [-2.39758091e-02, -3.66182392e-02, -1.42564510e-02],
               ...,
               [-2.57352036e-02, -1.30193541e-02, -1.42700677e-02],
               [-1.16573145e-02, -1.03436958e-02, -2.65486491e-03],
               [ 4.80652990e-02,  1.31812110e-02,  4.02105108e-02]],
      
              [[-4.04344934e-02, -3.59703964e-02, -3.45494651e-02],
               [-6.36351531e-02, -5.01866228e-02, -5.03541000e-02],
               [-2.18118174e-02, -2.24104271e-02, -1.87514300e-02],
               ...,
               [-2.07125734e-02, -1.93613847e-02, -1.90652796e-02],
               [-1.71725392e-02, -1.41379985e-02, -1.35063678e-02],
               [ 6.01759801e-02,  4.93910828e-02,  5.36831375e-02]],
      
              [[ 2.86682966e-02,  3.20268398e-02,  2.95692942e-02],
               [ 4.34325441e-02,  4.73849063e-02,  4.35284843e-02],
               [ 1.99255126e-02,  1.57083928e-02,  1.93408830e-02],
               ...,
      ...
               ...,
               [-2.69771117e-03, -3.64429604e-02, -3.27062402e-02],
               [-7.03103807e-04, -9.22475180e-03, -2.57338713e-02],
               [ 1.53851564e-01,  1.53041658e-01, -7.31188951e-03]],
      
              [[ 5.40793655e-03, -2.38576597e-04, -8.11218187e-06],
               [ 1.03659910e-02,  7.67184162e-03, -1.98821601e-03],
               [-7.38141253e-04, -8.13952392e-03, -1.55442008e-03],
               ...,
               [ 1.52258812e-03, -2.18115754e-03, -8.41467136e-04],
               [ 2.58704937e-03,  1.07263009e-03, -5.18633926e-05],
               [-1.26991250e-02, -1.22900297e-02,  7.60138700e-04]],
      
              [[ 1.12116387e-02,  1.17415215e-02,  1.12632551e-02],
               [ 1.62448204e-02,  1.71448738e-02,  1.54098057e-02],
               [ 8.47609120e-03,  8.30410186e-03,  7.59920840e-03],
               ...,
               [ 6.37787667e-03,  6.54341701e-03,  6.11904745e-03],
               [ 4.55178811e-03,  4.75105435e-03,  4.43108902e-03],
               [-1.37622991e-02, -1.54251835e-02, -1.42899188e-02]]]])

    • alpha_United Kingdom
      (chain, draw, equations)
      float64
      -0.105 -0.1099 ... -0.2986 -0.2771

      array([[[-0.10504847, -0.10987787, -0.11568448],
              [ 0.05049984,  0.06462595,  0.07323632],
              [ 0.20993419,  0.19883819,  0.19144551],
              ...,
              [ 0.04368448,  0.12319567,  0.05689683],
              [ 0.05776521,  0.01628855,  0.02436099],
              [-0.30739603, -0.2986272 , -0.27708257]]])

    • betaX_Ireland
      (chain, draw, betaX_Ireland_dim_0, betaX_Ireland_dim_1)
      float64
      -0.05636 -0.07013 ... 0.03163

      array([[[[-5.63613585e-02, -7.01316530e-02, -6.07409557e-02],
               [-7.25515457e-02, -8.76718177e-02, -7.97842750e-02],
               [-3.35471778e-02, -4.36230850e-02, -3.12771740e-02],
               ...,
               [-2.84617300e-02, -2.71654585e-02, -2.82291463e-02],
               [-1.30542441e-01, -1.43708806e-01, -1.49224861e-01],
               [-6.41395282e-02, -1.16062421e-01, -5.64768311e-02]],
      
              [[-7.58390921e-02, -7.40291967e-02, -7.16683955e-02],
               [-9.79737904e-02, -9.47430625e-02, -9.29247926e-02],
               [-4.43584884e-02, -4.15387463e-02, -3.80020949e-02],
               ...,
               [-2.78143551e-02, -2.78437093e-02, -2.50561363e-02],
               [-1.78090695e-01, -1.74201825e-01, -1.75912371e-01],
               [-1.12888189e-01, -9.96055527e-02, -9.29263820e-02]],
      
              [[ 5.83024323e-02,  5.87612745e-02,  5.83082381e-02],
               [ 7.41351914e-02,  7.57836883e-02,  7.48976492e-02],
               [ 3.80233060e-02,  3.32594997e-02,  3.44645598e-02],
               ...,
      ...
               ...,
               [ 6.82319001e-03, -6.97506458e-03, -1.45017860e-02],
               [-3.27922716e-01, -1.86692288e-01, -1.46732649e-01],
               [-2.23884865e-02, -1.32983562e-01, -9.27375381e-02]],
      
              [[ 2.90661497e-02,  1.13429741e-02,  1.04601173e-02],
               [ 3.25599336e-02,  1.78357114e-02,  1.61005972e-02],
               [ 1.33529018e-02,  3.72229383e-03,  1.03354929e-02],
               ...,
               [ 1.74939468e-02, -1.17313520e-03,  1.33576926e-04],
               [ 5.17234887e-02,  3.52299281e-02,  1.78026406e-02],
               [ 6.07970992e-03,  1.66774566e-02,  4.01917905e-02]],
      
              [[ 2.14802003e-02,  2.05715801e-02,  2.06112919e-02],
               [ 2.75169822e-02,  2.60570226e-02,  2.61178648e-02],
               [ 1.24896653e-02,  1.34676256e-02,  1.41815825e-02],
               ...,
               [ 7.84468179e-03,  8.97218835e-03,  1.01794491e-02],
               [ 4.97487964e-02,  4.26521968e-02,  4.17659545e-02],
               [ 3.29057445e-02,  3.49353835e-02,  3.16323974e-02]]]])

    • z_scale_alpha_South Africa
      (chain, draw)
      float64
      0.1016 0.1248 ... 0.1378 0.07456

      array([[0.10158372, 0.12483101, 0.51288006, 0.15688106, 0.36685966,
              0.1977919 , 0.15267253, 0.19591569, 0.59390305, 0.85488895,
              0.10587033, 0.21915306, 0.1623386 , 0.5986583 , 0.16613045,
              0.67263342, 0.11661068, 0.32518286, 1.5361486 , 1.45709589,
              0.1294471 , 0.47819553, 0.15264436, 0.44517857, 0.10923452,
              0.16646303, 0.10647573, 0.0892792 , 0.14177543, 0.27333858,
              0.13350324, 0.08810627, 0.26110173, 0.0919285 , 0.09816649,
              0.26209278, 0.0764066 , 0.04830488, 0.40724656, 0.12750582,
              0.31631358, 0.14794213, 0.37235809, 0.25241872, 0.12788007,
              0.13404573, 0.17880159, 0.36286645, 0.51347296, 0.15289694,
              0.21073588, 0.23397541, 0.43315221, 0.10431045, 0.5654643 ,
              0.41999103, 0.40271515, 0.15731881, 0.14442823, 0.12233247,
              0.54836549, 0.59848302, 0.2114371 , 0.26221595, 0.47246925,
              0.3137886 , 0.10494884, 0.12912805, 0.18391246, 0.12884373,
              0.15274523, 0.3725999 , 0.12177836, 0.24943004, 0.17295438,
              0.1309844 , 1.8084263 , 0.186108  , 0.15504212, 0.27137544,
              0.42143829, 0.19261572, 0.39520666, 0.22817145, 0.11095781,
              0.15273024, 0.50592954, 0.09639036, 0.06401957, 0.21317518,
              0.07973296, 0.17947608, 0.09611679, 0.29737776, 0.06023055,
              0.14621088, 0.16808568, 0.15571004, 0.12821163, 0.40133051,
      ...
              0.08203337, 0.45353632, 0.12209597, 0.16200809, 0.31780427,
              0.22325601, 0.11873745, 0.08931568, 0.14336465, 0.23646683,
              0.10727013, 0.09932834, 0.18313903, 0.10980764, 0.21582747,
              0.10017599, 0.09735297, 0.23616385, 0.14951644, 0.06934906,
              0.21301649, 0.11839936, 0.1319655 , 0.10892052, 0.22106444,
              0.47243188, 0.34067691, 0.11456418, 0.08852128, 0.15495958,
              0.22919555, 0.18288511, 0.34971504, 0.25516174, 0.1457496 ,
              0.39572965, 0.6039811 , 0.12686073, 0.17295965, 0.15575192,
              0.0565876 , 0.10520198, 0.21569628, 0.25940171, 0.63693879,
              0.18781137, 0.09305883, 0.25714287, 0.15878983, 0.44034101,
              0.11823393, 0.13136161, 0.20973821, 1.42332463, 0.21302649,
              0.2226954 , 0.27316585, 0.14044902, 0.53966122, 0.1195044 ,
              0.150667  , 0.23497026, 0.11131538, 0.20400561, 0.11954057,
              0.18559815, 0.30009964, 0.17376405, 0.16068921, 0.09253434,
              0.60062737, 0.2703372 , 0.07692366, 0.09411692, 0.26417048,
              0.09748224, 0.11672049, 0.13086781, 0.20560368, 0.20239755,
              0.08500308, 0.22931061, 0.11815733, 0.32180559, 0.2216965 ,
              0.72182278, 0.12920471, 0.34160552, 0.48694934, 0.31786736,
              0.18793372, 0.15005929, 0.20836772, 0.42221041, 0.12569971,
              0.16010514, 0.13736873, 0.30613186, 0.13783877, 0.07455761]])

    • omega_South Africa
      (chain, draw, omega_South Africa_dim_0, omega_South Africa_dim_1)
      float64
      1.784 0.0 0.0 ... -0.05803 0.6967

      array([[[[ 1.78358959,  0.        ,  0.        ],
               [ 0.18121283,  1.15854938,  0.        ],
               [-0.02083124,  0.02060528,  0.10876988]],
      
              [[ 1.99766962,  0.        ,  0.        ],
               [-0.4775523 ,  0.93489946,  0.        ],
               [-0.66727127, -0.56894271,  0.97454354]],
      
              [[ 0.6258802 ,  0.        ,  0.        ],
               [-0.05006584,  0.56308675,  0.        ],
               [-0.03356472, -0.11918844,  1.28177522]],
      
              ...,
      
              [[ 0.59207105,  0.        ,  0.        ],
               [-0.15405435,  1.15191665,  0.        ],
               [ 0.42015146, -0.13112777,  1.3176359 ]],
      
              [[ 0.94560191,  0.        ,  0.        ],
               [-0.19599059,  0.87824301,  0.        ],
               [-0.01612961,  0.1012689 ,  0.46264248]],
      
              [[ 1.50154014,  0.        ,  0.        ],
               [ 1.74863285,  0.3581054 ,  0.        ],
               [ 0.3241124 , -0.05803056,  0.6967033 ]]]])

    • z_scale_beta_United Kingdom
      (chain, draw)
      float64
      0.3233 0.1573 ... 0.1529 0.2527

      array([[0.32329421, 0.1573022 , 0.18395888, 0.31115335, 0.08793985,
              0.64458887, 0.08426981, 0.1739706 , 0.25291676, 0.40157056,
              0.1272336 , 0.2048703 , 0.82405807, 1.0602077 , 0.30134718,
              0.27591026, 0.11990954, 0.22748406, 0.1296425 , 0.03586132,
              0.18854633, 0.13555937, 0.15987621, 0.20211453, 0.96087343,
              0.13200587, 0.35302074, 0.16344653, 0.27828552, 0.0784578 ,
              0.20021474, 0.1040394 , 0.26592825, 0.15760564, 0.25392231,
              0.4902283 , 0.21793767, 0.48491566, 0.18729284, 0.30805642,
              0.32554183, 0.1028073 , 0.1974544 , 0.36962696, 0.12917224,
              0.11429995, 0.23014723, 0.12717217, 0.17021359, 0.42686837,
              0.51873028, 0.14007854, 0.1921737 , 0.138695  , 0.16323093,
              0.37369897, 0.28539739, 0.26873964, 0.16324976, 0.46518   ,
              0.15825429, 0.15334833, 0.11715296, 0.56726684, 0.3316949 ,
              0.22294716, 0.08289984, 0.20016843, 0.08728106, 0.36024453,
              0.4137913 , 0.21460476, 0.08989952, 0.62251973, 0.09447217,
              1.09391803, 0.18945414, 0.28841037, 0.13869962, 0.16524337,
              0.10166989, 0.05820755, 0.37717556, 0.16057303, 0.26310522,
              0.21005783, 0.34844353, 0.15838789, 0.15406413, 0.29755489,
              0.32437052, 0.41087799, 0.1377247 , 0.08347871, 0.50160563,
              0.113767  , 0.13644536, 0.09342668, 0.27791361, 0.17950133,
      ...
              0.11099167, 0.23969892, 0.12262426, 0.1755397 , 0.24322786,
              0.11843434, 0.38237235, 0.21831319, 0.05396117, 0.23099262,
              0.20061547, 0.19406781, 0.17941891, 0.08188348, 0.1880668 ,
              0.51481259, 0.20328566, 0.70005929, 0.15409202, 0.3034517 ,
              0.37492744, 0.12686545, 0.12791117, 0.67418773, 0.32532571,
              0.07088648, 0.32204798, 0.16968474, 0.17607128, 0.19494038,
              0.11102617, 0.18283606, 0.20243548, 0.35749114, 0.16571656,
              0.14121779, 0.34345642, 0.1701505 , 0.07026001, 0.44226981,
              0.17050301, 0.22328302, 0.22484323, 0.09580508, 0.33943649,
              0.32584451, 0.14876404, 0.56129836, 0.50985411, 0.20187562,
              0.27118215, 0.14051975, 0.15176628, 0.51159659, 0.19814433,
              0.32667369, 0.05378582, 0.07843321, 0.11752381, 0.10458065,
              0.11609248, 0.06791563, 0.29600561, 0.45469787, 0.11424575,
              0.18505702, 0.08807271, 0.19533745, 0.12638563, 0.10660988,
              0.09380297, 0.14078204, 0.05021521, 0.11993517, 0.30265546,
              0.24492029, 0.23754694, 0.12969476, 0.37838559, 0.26103451,
              0.57541725, 0.11774033, 0.90168756, 0.12440032, 0.12350289,
              0.18303855, 0.49137428, 0.17835225, 0.21784502, 0.14457128,
              0.08277858, 0.25047164, 0.14644423, 0.11178635, 0.08588925,
              0.18190685, 0.75139059, 0.51204172, 0.15293603, 0.25272013]])

    • noise_chol_Canada
      (chain, draw, noise_chol_Canada_dim_0)
      float64
      1.104 -0.06141 ... 0.3915 0.9881

      array([[[ 1.10440523e+00, -6.14109927e-02,  8.22749881e-01,
                1.02356729e-01, -3.51431230e-02,  1.75236206e+00],
              [ 1.58393068e-01, -2.09363094e-01,  1.81394898e+00,
               -1.47916702e-02,  1.84719694e-03,  1.02419234e-01],
              [ 1.08584398e-01, -3.50908298e-01,  2.43234781e+00,
               -2.89296391e-02, -1.37607379e-01,  1.16846656e+00],
              ...,
              [ 6.75563536e-01, -2.71357075e-01,  3.83127860e+00,
                5.39568575e-01,  7.32348991e-02,  1.76801481e+00],
              [ 3.21172324e+00,  1.80240754e-02,  1.19982287e+00,
                8.23736425e-02,  2.21532656e-01,  1.48254113e+00],
              [ 9.42435758e-01, -2.09670521e-01,  5.32329692e-01,
               -3.01572098e-01,  3.91459628e-01,  9.88126253e-01]]])

    • beta_hat_scale
      (chain, draw)
      float64
      0.445 0.253 ... 0.2568 0.04878

      array([[0.44503705, 0.25302872, 0.09734064, 0.08140516, 0.09403591,
              0.53281248, 0.28569491, 0.06927693, 0.23716861, 0.48898782,
              0.12018069, 0.32561429, 0.11594634, 0.11938186, 0.18987112,
              0.05024414, 0.31705729, 0.36470701, 0.23925633, 0.13041001,
              0.82218282, 0.08605663, 0.43065183, 0.43511532, 0.42329363,
              0.23868226, 0.14223661, 0.18942365, 0.11064443, 0.17979744,
              0.08929333, 0.08621157, 0.22297356, 0.32616151, 0.42752162,
              0.33973567, 0.26361747, 0.33651065, 0.30514592, 0.6040292 ,
              0.30559007, 0.2764355 , 0.1030149 , 0.2478419 , 0.1149303 ,
              0.17284634, 0.12390858, 0.11802487, 0.12523576, 0.08518932,
              0.24107197, 0.20765158, 0.17661285, 0.27904944, 0.23839197,
              0.48257666, 0.09528768, 0.11454373, 0.29407864, 0.26232946,
              0.75598757, 0.16745614, 0.11830287, 0.10899471, 0.27860523,
              0.20970053, 0.19249533, 0.13234794, 0.10192466, 0.05061725,
              0.09358496, 0.16118725, 0.09068751, 0.16353462, 0.14521383,
              0.1080347 , 0.20866713, 0.24090732, 0.43486484, 0.18934286,
              0.23082179, 0.24133749, 0.1685625 , 0.06079055, 0.23491592,
              0.21468027, 0.12939244, 0.32378068, 0.21257374, 0.17706071,
              0.14395569, 0.3012523 , 0.08673807, 0.20119311, 0.24151278,
              1.02288321, 0.21913009, 0.11876808, 0.13561561, 0.22144594,
      ...
              0.38661143, 0.49959209, 0.33899083, 0.28879166, 0.16437471,
              0.25944415, 0.26070646, 0.14659932, 0.2987469 , 0.16546793,
              0.54347232, 0.15610741, 0.32850537, 0.14202903, 0.46403254,
              0.20134906, 0.14092558, 0.31915747, 0.1083041 , 0.06595824,
              0.12607071, 0.32347699, 0.18128918, 0.20217098, 0.15515703,
              0.07901812, 0.0957816 , 0.69466819, 0.17602688, 0.14354201,
              0.15914825, 0.27937793, 0.35717692, 0.25445324, 0.06645117,
              0.52638452, 0.28862398, 0.182403  , 0.10244508, 0.28279983,
              0.20290727, 0.67652985, 0.19440047, 0.07835929, 0.25447417,
              0.09081237, 0.13050397, 0.12495608, 0.89505844, 0.2964415 ,
              0.12699845, 0.31185433, 0.21496858, 0.13297115, 0.0998401 ,
              0.17609794, 0.24341781, 0.49670671, 0.38368282, 0.11393543,
              0.08738413, 0.14064452, 0.14818658, 0.21655171, 0.26690996,
              0.28877758, 0.12789248, 0.17698881, 0.06163298, 0.21681181,
              0.10022167, 0.6127    , 0.18760715, 0.16731792, 0.14341602,
              0.1900311 , 0.12648602, 0.0819759 , 0.18701306, 0.53192278,
              0.08351364, 0.17312503, 0.19946883, 0.21985174, 0.07079137,
              0.28623224, 0.15362624, 0.18702488, 0.61049313, 0.36899625,
              0.10071906, 0.07739268, 0.24766829, 0.11793443, 0.13010391,
              0.17038084, 0.07135453, 1.03649588, 0.25679807, 0.04878009]])

    • omega_global_corr
      (chain, draw, omega_global_corr_dim_0, omega_global_corr_dim_1)
      float64
      1.0 0.2969 -0.2592 ... 0.4423 1.0

      array([[[[ 1.        ,  0.29692789, -0.25923662],
               [ 0.29692789,  1.        ,  0.14574549],
               [-0.25923662,  0.14574549,  1.        ]],
      
              [[ 1.        , -0.50390112, -0.88406178],
               [-0.50390112,  1.        ,  0.05741437],
               [-0.88406178,  0.05741437,  1.        ]],
      
              [[ 1.        ,  0.34143595,  0.08368607],
               [ 0.34143595,  1.        , -0.65070387],
               [ 0.08368607, -0.65070387,  1.        ]],
      
              ...,
      
              [[ 1.        , -0.27433149,  0.10919589],
               [-0.27433149,  1.        , -0.6416615 ],
               [ 0.10919589, -0.6416615 ,  1.        ]],
      
              [[ 1.        , -0.71381744, -0.6416458 ],
               [-0.71381744,  1.        ,  0.01697827],
               [-0.6416458 ,  0.01697827,  1.        ]],
      
              [[ 1.        ,  0.99169239,  0.45199652],
               [ 0.99169239,  1.        ,  0.44227972],
               [ 0.45199652,  0.44227972,  1.        ]]]])

    • z_scale_beta_Chile
      (chain, draw)
      float64
      0.3099 0.319 ... 0.1535 0.249

      array([[0.30990536, 0.31898127, 0.46805575, 1.46775288, 0.31189055,
              0.29670148, 0.12160982, 0.21345929, 0.28993789, 0.07594419,
              0.17217328, 0.14362066, 0.42858227, 0.18093675, 0.31762323,
              0.08629456, 0.08945899, 0.12837699, 0.30115755, 0.24399574,
              0.17697334, 0.0704102 , 0.19864746, 0.37872674, 0.18952204,
              0.17068355, 0.06265502, 0.35056743, 0.16200572, 0.16669569,
              0.12729406, 0.17905708, 0.12424471, 0.19146932, 0.32778996,
              0.22980471, 0.2034019 , 0.14299723, 0.07957804, 0.12835942,
              0.13764474, 0.11565458, 0.26232806, 0.14814521, 0.06457627,
              0.12113411, 0.142652  , 0.14084364, 0.21478267, 0.32992681,
              0.2477339 , 0.21158255, 0.5724395 , 0.25254504, 0.4214072 ,
              0.1466429 , 0.43787646, 0.07259178, 0.56152386, 0.27947568,
              1.55597931, 0.12504306, 0.11720669, 0.28814203, 0.23095757,
              0.59749398, 0.19761514, 0.10450226, 0.25204799, 0.23369357,
              0.59321525, 0.11224511, 0.14313231, 0.1937793 , 0.72057527,
              0.12585264, 0.09828015, 0.1590817 , 0.33499431, 0.15217841,
              0.92295021, 0.51095889, 0.27241345, 0.25733832, 0.06198806,
              0.1485592 , 0.20171744, 0.36242288, 0.18339561, 0.15778783,
              0.40656022, 0.13442682, 0.35546348, 0.53646324, 0.22447086,
              0.22082826, 0.35280804, 0.28602613, 0.25661764, 0.18910331,
      ...
              0.17809947, 0.36406137, 0.10420537, 0.08386398, 0.13171774,
              0.1779471 , 0.25193476, 0.07719311, 0.25698288, 0.07146643,
              0.19145748, 0.07357926, 0.18635246, 0.30343246, 0.152774  ,
              0.18638894, 0.46796965, 0.50509979, 0.10939796, 0.35368413,
              0.10356129, 0.18410041, 0.16715199, 0.19867206, 0.34242053,
              0.15595651, 0.34579875, 0.13957914, 0.13643082, 0.32962603,
              0.44742806, 0.12325874, 0.24707   , 0.20842144, 0.15227183,
              0.18973992, 0.08675561, 0.40103028, 0.15597983, 0.0843263 ,
              0.39750353, 0.11267465, 0.13539262, 0.60783435, 0.13182377,
              0.40304187, 0.09901869, 0.21478436, 1.25552176, 0.15233609,
              0.20822934, 0.26070483, 0.18185246, 0.14669762, 0.08624216,
              0.07059232, 0.28667757, 0.1052545 , 0.27464558, 0.95117541,
              0.48424707, 0.15908758, 0.46374762, 0.19377645, 0.07026614,
              0.47954379, 0.27252315, 0.09018434, 0.09685043, 0.74444211,
              0.14658351, 0.20068838, 0.17096532, 0.1126428 , 0.63954626,
              0.53113693, 0.38469789, 0.221623  , 0.18916632, 0.06957461,
              0.09160466, 0.05415353, 0.20477535, 0.19636591, 0.21163338,
              0.04727546, 0.42889752, 1.94669786, 0.47964026, 0.26143897,
              0.08786324, 0.12047803, 0.15553462, 0.17466272, 0.65884565,
              0.14780694, 0.14465865, 0.2293884 , 0.15349672, 0.24900105]])

    • betaX_Australia
      (chain, draw, betaX_Australia_dim_0, betaX_Australia_dim_1)
      float64
      -0.02716 -0.04112 ... 7.089e-05

      array([[[[-2.71631337e-02, -4.11209056e-02, -2.06149307e-02],
               [-2.37026713e-02, -3.87175835e-02, -1.67115989e-02],
               [-2.68779372e-02, -5.04349934e-02, -1.89863050e-02],
               ...,
               [-1.76051608e-02, -3.32686837e-02, -1.21494546e-02],
               [-1.95325150e-02, -2.38321889e-02, -1.56259155e-02],
               [-6.34610944e-03,  4.72511321e-03, -4.29248487e-03]],
      
              [[-4.57268446e-02, -4.48644831e-02, -4.31727789e-02],
               [-4.27550145e-02, -4.17061760e-02, -4.03159647e-02],
               [-4.99334261e-02, -4.88492687e-02, -4.69735667e-02],
               ...,
               [-3.42849440e-02, -3.24920082e-02, -3.16742955e-02],
               [-2.80948391e-02, -2.87194875e-02, -2.71145462e-02],
               [-1.75129213e-03, -1.15958062e-03, -2.66442705e-04]],
      
              [[ 3.66348357e-02,  3.60079149e-02,  3.46216391e-02],
               [ 3.45002324e-02,  3.39491167e-02,  3.26298453e-02],
               [ 3.98914082e-02,  3.92686230e-02,  3.78749625e-02],
               ...,
      ...
               ...,
               [-3.93991174e-02, -3.25176960e-02, -1.39060936e-02],
               [-1.84757090e-02, -3.13568524e-02, -1.07089047e-02],
               [-1.91136119e-03, -1.30694417e-03,  1.82679994e-03]],
      
              [[ 5.41213322e-03,  2.23393602e-03,  2.23527329e-03],
               [ 5.14878836e-03,  2.14668584e-03,  2.41120458e-03],
               [ 5.82424046e-03,  1.83661445e-03,  3.07894010e-03],
               ...,
               [ 4.40988044e-03,  1.03347356e-03,  2.96765783e-03],
               [ 2.68659013e-03,  2.06077366e-03, -9.73468885e-05],
               [-2.74763707e-04,  1.61254037e-03, -5.17438623e-04]],
      
              [[ 1.33079716e-02,  1.18015094e-02,  1.28730283e-02],
               [ 1.23619639e-02,  1.10674498e-02,  1.21157449e-02],
               [ 1.44231024e-02,  1.34265145e-02,  1.42602060e-02],
               ...,
               [ 9.88310291e-03,  9.24608458e-03,  9.57381238e-03],
               [ 8.17092213e-03,  6.82380882e-03,  7.99997718e-03],
               [-3.12477776e-04, -2.25905479e-04,  7.08883444e-05]]]])

    • noise_chol_Canada_corr
      (chain, draw, noise_chol_Canada_corr_dim_0, noise_chol_Canada_corr_dim_1)
      float64
      1.0 -0.07443 0.0583 ... 0.4297 1.0

      array([[[[ 1.        , -0.07443409,  0.05829965],
               [-0.07443409,  1.        , -0.02430053],
               [ 0.05829965, -0.02430053,  1.        ]],
      
              [[ 1.        , -0.11465723, -0.14291699],
               [-0.11465723,  1.        ,  0.03411636],
               [-0.14291699,  0.03411636,  1.        ]],
      
              [[ 1.        , -0.14278903, -0.02458128],
               [-0.14278903,  1.        , -0.11221584],
               [-0.02458128, -0.11221584,  1.        ]],
      
              ...,
      
              [[ 1.        , -0.07064978,  0.29166406],
               [-0.07064978,  1.        ,  0.01888224],
               [ 0.29166406,  0.01888224,  1.        ]],
      
              [[ 1.        ,  0.01502059,  0.05486956],
               [ 0.01502059,  1.        ,  0.14837172],
               [ 0.05486956,  0.14837172,  1.        ]],
      
              [[ 1.        , -0.36647139, -0.27296569],
               [-0.36647139,  1.        ,  0.42971006],
               [-0.27296569,  0.42971006,  1.        ]]]])

    • alpha_hat_location
      (chain, draw)
      float64
      -0.1142 0.06737 ... 0.06274 -0.2666

      array([[-1.14215881e-01,  6.73702220e-02,  1.91390197e-01,
              -1.16041416e-02, -1.24930644e-02,  1.73151022e-01,
               1.62079891e-02, -9.84983370e-02, -1.83338972e-01,
               2.73037779e-02,  8.03824509e-02, -7.74581290e-02,
              -2.33151633e-01,  2.11686594e-01, -1.26425955e-01,
               1.92428012e-01,  3.05683152e-02, -5.16687825e-02,
               3.15888205e-01, -1.57532143e-01,  1.22378583e-01,
              -1.08112679e-01,  5.23449912e-02,  4.31351949e-02,
              -1.42511344e-02,  5.19508807e-02,  1.92124314e-02,
               1.28942591e-02, -7.49653882e-03,  1.90296410e-01,
              -7.17142579e-02, -6.71235689e-02, -7.51747078e-02,
               1.11586049e-01,  7.90522444e-02, -1.18764713e-01,
               1.19181240e-01,  9.75056361e-02, -5.54103362e-02,
              -1.33069569e-01,  1.36178519e-01,  4.87806046e-02,
               3.33680523e-02, -5.04320820e-02, -1.11918471e-01,
               1.56954740e-02, -6.11651521e-02, -3.15021225e-02,
               1.10610591e-01,  1.81375319e-03,  1.09281481e-01,
              -4.78632564e-02,  1.81503756e-01,  1.02128533e-01,
              -1.08703136e-01, -1.19687776e-01,  2.21152009e-01,
               2.57520351e-02,  2.38293206e-01,  1.39071621e-01,
      ...
               8.16216513e-02, -3.45893522e-02, -1.10124812e-01,
               7.01522725e-02, -1.21726161e-01, -1.47423865e-01,
              -1.23039680e-01, -1.23374131e-02, -1.19147263e-02,
               1.07446992e-01, -9.88817692e-02, -1.45182600e-01,
               1.93775170e-01, -1.27346943e-01,  1.86633137e-02,
               1.30837905e-01, -4.27720196e-02, -4.25461514e-02,
              -2.19099141e-03,  1.54280390e-01,  1.13050168e-01,
              -7.06144502e-02,  2.57282628e-01, -3.94247200e-02,
               2.39564231e-02, -7.92104464e-02, -4.87981362e-02,
              -7.78851583e-03, -2.28206362e-01, -1.18388960e-02,
              -1.91268194e-02,  9.57533367e-02, -1.09828713e-02,
              -4.72533983e-02, -4.23669224e-03, -2.92308657e-01,
               1.61615890e-01,  1.61840033e-01, -1.32490938e-01,
              -5.74908350e-02,  1.19546422e-02, -9.28351294e-02,
              -2.93992019e-02,  1.14365769e-01, -1.27576497e-01,
               9.93977785e-02, -5.33986035e-02,  7.83101625e-02,
               8.45049729e-02, -3.99923331e-03,  1.85768987e-02,
              -4.76808205e-02, -1.72594705e-03, -1.78767313e-01,
              -3.48304267e-02,  1.45269570e-01,  5.70227246e-02,
               6.27400545e-02, -2.66605418e-01]])

    • noise_chol_Chile_stds
      (chain, draw, noise_chol_Chile_stds_dim_0)
      float64
      0.02867 0.4035 ... 1.622 0.3862

      array([[[2.86658712e-02, 4.03513734e-01, 8.40480985e-01],
              [1.96448849e-01, 4.25975528e-01, 4.36350422e-01],
              [4.93996180e+00, 7.06556201e-01, 2.40882351e+00],
              ...,
              [3.05380895e-03, 3.52957975e+00, 2.20274432e-01],
              [1.79712235e-01, 1.09227714e+00, 1.62611114e+00],
              [3.08303752e-01, 1.62203664e+00, 3.86181427e-01]]])

    • noise_chol_United Kingdom
      (chain, draw, noise_chol_United Kingdom_dim_0)
      float64
      0.03717 0.858 ... 0.1135 0.8889

      array([[[ 3.71684705e-02,  8.58028852e-01,  2.48402104e+00,
               -5.57011125e-04, -8.38986884e-04,  1.60835183e-03],
              [ 5.13831503e-01,  2.34162679e-01,  9.29773075e-01,
               -1.20742517e-01,  5.56586464e-01,  6.70103597e-01],
              [ 4.04689556e-01, -1.14194737e-01,  2.20613660e-01,
               -5.65167465e-02, -2.36675135e-02,  1.95619011e-01],
              ...,
              [ 1.62342154e+00,  2.91640489e-02,  9.95349212e-01,
                2.90955246e-03, -3.25260129e-03,  1.13630417e-01],
              [ 2.92163436e-01, -1.05168710e-01,  2.21772073e-01,
               -1.17963943e-02, -2.78526733e-02,  5.06171702e-01],
              [ 2.76772440e+00, -1.28202638e-01,  3.84651102e-01,
               -2.57575151e-01,  1.13514286e-01,  8.88888728e-01]]])

    • noise_chol_Australia
      (chain, draw, noise_chol_Australia_dim_0)
      float64
      3.44 -0.002917 ... 0.03687 0.108

      array([[[ 3.44031341e+00, -2.91742222e-03,  2.95114501e-01,
                3.00258616e-02,  2.99474003e-01,  5.51796129e-01],
              [ 3.95364961e+00,  8.45824247e-01,  1.97179631e+00,
                7.70370867e-02, -3.40942505e-01,  1.11409713e+00],
              [ 1.69569723e-01,  7.43677258e-03,  1.00132117e+00,
                5.33000539e-02, -8.73193794e-03,  2.80895870e-01],
              ...,
              [ 5.26884235e-01, -2.75655607e-03,  2.60203450e-02,
               -4.26425806e-05,  1.02798877e-02,  3.36273249e-02],
              [ 1.49509349e+00,  1.57323061e-02,  1.18061170e-01,
                7.93359128e-03,  1.79957435e-01,  2.16257204e+00],
              [ 1.14331405e+00, -1.66588331e-01,  6.64254119e-01,
                1.37794637e-03,  3.68710103e-02,  1.08048111e-01]]])

    • betaX_New Zealand
      (chain, draw, betaX_New Zealand_dim_0, betaX_New Zealand_dim_1)
      float64
      0.0138 0.005566 ... 0.01215 0.01206

      array([[[[ 0.01379526,  0.00556591,  0.01453189],
               [-0.01093608, -0.00610566,  0.00132908],
               [-0.0654455 , -0.05485527, -0.05683577],
               ...,
               [-0.04833221, -0.04626699, -0.04100381],
               [-0.04691773, -0.04578927, -0.0457036 ],
               [-0.03383016, -0.03411925, -0.03302587]],
      
              [[ 0.01074248,  0.00809032,  0.00140507],
               [ 0.00125393,  0.00577161,  0.00471226],
               [-0.06928569, -0.0540019 , -0.04032888],
               ...,
               [-0.04526051, -0.04856437, -0.04233282],
               [-0.05114788, -0.05350525, -0.0469331 ],
               [-0.0363158 , -0.04021684, -0.03642858]],
      
              [[-0.00549983, -0.00797334, -0.00876304],
               [-0.000499  , -0.00053982,  0.00104204],
               [ 0.04512627,  0.04957843,  0.05111695],
               ...,
      ...
               ...,
               [-0.05104744, -0.04843079, -0.04806802],
               [-0.05096372, -0.05555819, -0.04730662],
               [-0.03881188, -0.04276146, -0.03506456]],
      
              [[-0.00072227, -0.00092834,  0.00109428],
               [ 0.00307515, -0.00035414, -0.00106262],
               [ 0.00512026,  0.00298923,  0.00551994],
               ...,
               [ 0.00556997,  0.00053438,  0.00740147],
               [ 0.0040398 ,  0.00120579,  0.00761817],
               [ 0.00299686,  0.0006392 ,  0.00617203]],
      
              [[-0.00330571, -0.00312396, -0.00234554],
               [ 0.00028601,  0.00025555,  0.00100261],
               [ 0.01756795,  0.01793027,  0.01740211],
               ...,
               [ 0.01437661,  0.0152307 ,  0.01547717],
               [ 0.01510083,  0.01617478,  0.01592912],
               [ 0.01122486,  0.01215329,  0.01205646]]]])

    • lag_coefs_Chile
      (chain, draw, equations, lags, cross_vars)
      float64
      -0.1921 -0.1453 ... 0.04501 0.05681

      array([[[[[-0.19213101, -0.14533614, -0.06473391],
                [-0.10356245, -0.36552089, -0.43861718]],
      
               [[ 0.11692234, -0.50634091, -0.25130411],
                [-0.10260963,  0.03150801, -0.12869279]],
      
               [[-0.00281497, -0.19004161, -0.25181706],
                [-0.02282547, -0.17534982, -0.06769479]]],
      
      
              [[[-0.13170617, -0.16964863, -0.36087602],
                [-0.13553971, -0.3571018 , -0.23857882]],
      
               [[-0.2724737 , -0.32146061, -0.18594359],
                [-0.24326934, -0.27428855, -0.16527453]],
      
               [[-0.33820013, -0.12477845, -0.25843155],
                [-0.1160043 , -0.2363186 , -0.11849807]]],
      
      
      ...
      
      
              [[[ 0.06922752,  0.00624961, -0.01264068],
                [ 0.0254135 ,  0.09469037, -0.02588675]],
      
               [[-0.00340065,  0.01196188,  0.05139274],
                [-0.00997527,  0.03844669, -0.02156547]],
      
               [[ 0.08087667,  0.05921484, -0.0042421 ],
                [ 0.07486357,  0.04012774, -0.01098364]]],
      
      
              [[[ 0.0683015 ,  0.06817381,  0.06101953],
                [ 0.05036844,  0.0645917 ,  0.07088023]],
      
               [[ 0.09482449,  0.05084338,  0.0451617 ],
                [ 0.05136685,  0.07126498,  0.08353124]],
      
               [[ 0.05112117,  0.07426872,  0.05209611],
                [ 0.06962942,  0.0450149 ,  0.05680818]]]]])

    • noise_chol_Australia_corr
      (chain, draw, noise_chol_Australia_corr_dim_0, noise_chol_Australia_corr_dim_1)
      float64
      1.0 -0.009885 ... 0.3103 1.0

      array([[[[ 1.        , -0.00988525,  0.04777064],
               [-0.00988525,  1.        ,  0.47596262],
               [ 0.04777064,  0.47596262,  1.        ]],
      
              [[ 1.        ,  0.39422195,  0.06597661],
               [ 0.39422195,  1.        , -0.24233587],
               [ 0.06597661, -0.24233587,  1.        ]],
      
              [[ 1.        ,  0.00742676,  0.18633691],
               [ 0.00742676,  1.        , -0.02914212],
               [ 0.18633691, -0.02914212,  1.        ]],
      
              ...,
      
              [[ 1.        , -0.10534898, -0.00121269],
               [-0.10534898,  1.        ,  0.29084598],
               [-0.00121269,  0.29084598,  1.        ]],
      
              [[ 1.        ,  0.13208796,  0.00365593],
               [ 0.13208796,  1.        ,  0.08268365],
               [ 0.00365593,  0.08268365,  1.        ]],
      
              [[ 1.        , -0.24325681,  0.0120688 ],
               [-0.24325681,  1.        ,  0.31030004],
               [ 0.0120688 ,  0.31030004,  1.        ]]]])

    • omega_Canada
      (chain, draw, omega_Canada_dim_0, omega_Canada_dim_1)
      float64
      1.523 0.0 0.0 ... 0.1349 1.041

      array([[[[ 1.52328406e+00,  0.00000000e+00,  0.00000000e+00],
               [ 1.93627565e-02,  6.19236831e-01,  0.00000000e+00],
               [ 3.13928098e-02,  2.84468516e-03,  1.04516595e+00]],
      
              [[ 1.03567362e+00,  0.00000000e+00,  0.00000000e+00],
               [-5.51794742e-01,  1.39182387e+00,  0.00000000e+00],
               [-7.72412381e-01, -3.89664344e-01,  1.43258294e-01]],
      
              [[ 1.30713651e-01,  0.00000000e+00,  0.00000000e+00],
               [-1.80048623e-01,  1.71157986e+00,  0.00000000e+00],
               [-5.11170658e-03, -2.07499688e-01,  8.71055067e-01]],
      
              ...,
      
              [[ 5.99543140e-01,  0.00000000e+00,  0.00000000e+00],
               [-1.81476036e-01,  2.28719555e+00,  0.00000000e+00],
               [ 3.28976088e-01, -7.25345051e-02,  1.15105894e+00]],
      
              [[ 3.35607916e+00,  0.00000000e+00,  0.00000000e+00],
               [-2.57181861e-01,  1.25547820e+00,  0.00000000e+00],
               [ 5.13457700e-02,  1.66310933e-01,  1.23280455e+00]],
      
              [[ 1.83514675e+00,  0.00000000e+00,  0.00000000e+00],
               [ 1.62396274e+00,  4.49527903e-01,  0.00000000e+00],
               [ 1.85610003e-01,  1.34895216e-01,  1.04143226e+00]]]])

    • lag_coefs_Canada
      (chain, draw, equations, lags, cross_vars)
      float64
      -0.04739 -0.1423 ... 0.06879

      array([[[[[-0.04738794, -0.14234143, -0.13853129],
                [-0.21672458, -0.22407083, -0.13756053]],
      
               [[-0.01232171, -0.20316328, -0.12326586],
                [-0.09032331, -0.26726072, -0.26274655]],
      
               [[-0.16732872, -0.17919546, -0.02832849],
                [-0.31048545, -0.1777181 , -0.08124112]]],
      
      
              [[[-0.19777672, -0.18399189, -0.23498679],
                [-0.18921315, -0.2419562 , -0.175745  ]],
      
               [[-0.2598466 , -0.21769632, -0.21247609],
                [-0.1577351 , -0.16856828, -0.21739963]],
      
               [[-0.23133308, -0.18661768, -0.19154727],
                [-0.27220409, -0.2292755 , -0.24996292]]],
      
      
      ...
      
      
              [[[-0.056478  , -0.06623036, -0.04319848],
                [ 0.0013269 ,  0.04519498,  0.03744916]],
      
               [[ 0.06816514,  0.00815985,  0.02599815],
                [ 0.0353851 ,  0.00424746,  0.06376147]],
      
               [[-0.08474669,  0.00093978,  0.02174443],
                [ 0.0326497 , -0.02543293,  0.01845534]]],
      
      
              [[[ 0.06552367,  0.04694831,  0.05054006],
                [ 0.06591855,  0.05434666,  0.05416537]],
      
               [[ 0.05667259,  0.06613503,  0.06163121],
                [ 0.05148675,  0.0603007 ,  0.07082295]],
      
               [[ 0.05292572,  0.0572092 ,  0.07033403],
                [ 0.05395109,  0.06972252,  0.06879022]]]]])

    • alpha_Australia
      (chain, draw, equations)
      float64
      -0.1104 -0.1173 ... -0.3236 -0.2169

      array([[[-0.11040217, -0.11730994, -0.11892907],
              [ 0.07011581,  0.01573795,  0.04269177],
              [ 0.14804868,  0.37001871,  0.34760741],
              ...,
              [ 0.06043768,  0.03483796,  0.07371805],
              [ 0.12422274,  0.07173644,  0.06389303],
              [-0.18801587, -0.32364038, -0.21688848]]])

    • alpha_Ireland
      (chain, draw, equations)
      float64
      -0.1087 -0.1638 ... -0.1815 -0.2331

      array([[[-0.10869618, -0.163818  , -0.08208925],
              [ 0.07940262,  0.06773777,  0.09363815],
              [ 0.15238541,  0.16961705,  0.19856246],
              ...,
              [ 0.06369923, -0.01606961,  0.43712469],
              [ 0.04537984,  0.06825317,  0.03096073],
              [-0.19148377, -0.1815312 , -0.23313313]]])

    • noise_chol_Australia_stds
      (chain, draw, noise_chol_Australia_stds_dim_0)
      float64
      3.44 0.2951 ... 0.6848 0.1142

      array([[[3.44031341, 0.29512892, 0.62854212],
              [3.95364961, 2.14555339, 1.16764246],
              [0.16956972, 1.00134879, 0.28604131],
              ...,
              [0.52688423, 0.02616595, 0.03516354],
              [1.49509349, 0.11910477, 2.17006116],
              [1.14331405, 0.68482495, 0.11417427]]])

    • noise_chol_South Africa_corr
      (chain, draw, noise_chol_South Africa_corr_dim_0, noise_chol_South Africa_corr_dim_1)
      float64
      1.0 0.1287 0.1772 ... -0.275 1.0

      array([[[[ 1.00000000e+00,  1.28741931e-01,  1.77185626e-01],
               [ 1.28741931e-01,  1.00000000e+00, -4.56917382e-02],
               [ 1.77185626e-01, -4.56917382e-02,  1.00000000e+00]],
      
              [[ 1.00000000e+00,  1.01205065e-01,  1.13460593e-01],
               [ 1.01205065e-01,  1.00000000e+00, -1.89025777e-01],
               [ 1.13460593e-01, -1.89025777e-01,  1.00000000e+00]],
      
              [[ 1.00000000e+00, -2.21417734e-01, -4.03579898e-02],
               [-2.21417734e-01,  1.00000000e+00,  8.04885336e-03],
               [-4.03579898e-02,  8.04885336e-03,  1.00000000e+00]],
      
              ...,
      
              [[ 1.00000000e+00, -1.19892356e-01,  3.21335276e-01],
               [-1.19892356e-01,  1.00000000e+00, -5.17565248e-02],
               [ 3.21335276e-01, -5.17565248e-02,  1.00000000e+00]],
      
              [[ 1.00000000e+00,  1.23432754e-01,  8.48505149e-04],
               [ 1.23432754e-01,  1.00000000e+00,  2.50079003e-01],
               [ 8.48505149e-04,  2.50079003e-01,  1.00000000e+00]],
      
              [[ 1.00000000e+00,  2.50513196e-01,  1.19002911e-01],
               [ 2.50513196e-01,  1.00000000e+00, -2.75026897e-01],
               [ 1.19002911e-01, -2.75026897e-01,  1.00000000e+00]]]])

    • noise_chol_Ireland
      (chain, draw, noise_chol_Ireland_dim_0)
      float64
      3.052 0.654 ... 0.07744 0.5409

      array([[[ 3.05179578e+00,  6.54018601e-01,  2.16628875e+00,
               -5.36283083e-02,  4.41811696e-03,  1.73968325e-01],
              [ 6.47545198e-01, -1.91753318e-02,  7.77718888e-01,
               -1.56506280e-02, -2.60786049e-02,  1.43761624e-01],
              [ 7.07637200e-01, -2.23806635e-02,  2.20859235e+00,
               -1.46181329e-01,  6.40742541e-02,  4.46789597e-01],
              ...,
              [ 1.20541287e+00, -9.71924165e-02,  1.17056953e+00,
                4.81963023e-01, -4.65291663e-01,  2.62150833e+00],
              [ 1.56463364e+00,  7.99916182e-02,  6.06490213e-01,
               -1.01729349e-03,  1.99537798e-01,  1.01884394e+00],
              [ 1.21394237e+00,  8.46768355e-02,  4.19133586e-01,
                9.16616344e-02,  7.74371047e-02,  5.40857144e-01]]])

    • noise_chol_Ireland_corr
      (chain, draw, noise_chol_Ireland_corr_dim_0, noise_chol_Ireland_corr_dim_1)
      float64
      1.0 0.289 -0.2945 ... 0.1698 1.0

      array([[[[ 1.00000000e+00,  2.89022671e-01, -2.94498852e-01],
               [ 2.89022671e-01,  1.00000000e+00, -6.18902857e-02],
               [-2.94498852e-01, -6.18902857e-02,  1.00000000e+00]],
      
              [[ 1.00000000e+00, -2.46483740e-02, -1.06507675e-01],
               [-2.46483740e-02,  1.00000000e+00, -1.74794330e-01],
               [-1.06507675e-01, -1.74794330e-01,  1.00000000e+00]],
      
              [[ 1.00000000e+00, -1.01329313e-02, -3.08111964e-01],
               [-1.01329313e-02,  1.00000000e+00,  1.38166893e-01],
               [-3.08111964e-01,  1.38166893e-01,  1.00000000e+00]],
      
              ...,
      
              [[ 1.00000000e+00, -8.27452920e-02,  1.78125390e-01],
               [-8.27452920e-02,  1.00000000e+00, -1.86113264e-01],
               [ 1.78125390e-01, -1.86113264e-01,  1.00000000e+00]],
      
              [[ 1.00000000e+00,  1.30760250e-01, -9.79862682e-04],
               [ 1.30760250e-01,  1.00000000e+00,  1.90417587e-01],
               [-9.79862682e-04,  1.90417587e-01,  1.00000000e+00]],
      
              [[ 1.00000000e+00,  1.98027405e-01,  1.65451839e-01],
               [ 1.98027405e-01,  1.00000000e+00,  1.69772100e-01],
               [ 1.65451839e-01,  1.69772100e-01,  1.00000000e+00]]]])

    • betaX_Chile
      (chain, draw, betaX_Chile_dim_0, betaX_Chile_dim_1)
      float64
      -0.03785 0.01646 ... -0.01037

      array([[[[-0.03785033,  0.01645857,  0.02087206],
               [ 0.09531856,  0.07028343,  0.02932705],
               [ 0.05980812,  0.04857091,  0.00052036],
               ...,
               [-0.01685545, -0.02523695, -0.02725142],
               [-0.05015806, -0.02501123, -0.02422215],
               [ 0.00575774,  0.04877649,  0.03458518]],
      
              [[ 0.01966734, -0.03028052,  0.01579705],
               [ 0.06804103,  0.06359205,  0.05134099],
               [ 0.00193208,  0.0490178 , -0.00721928],
               ...,
               [-0.04087721, -0.04169082, -0.04024195],
               [-0.05170266, -0.04250768, -0.03567257],
               [ 0.04181574,  0.04772947,  0.04759498]],
      
              [[ 0.00658565,  0.00798913,  0.03706616],
               [-0.04220304, -0.06184718, -0.05100309],
               [-0.01072383, -0.02186942, -0.0499245 ],
               ...,
      ...
               ...,
               [-0.04834585, -0.01974106, -0.00777098],
               [-0.0127852 , -0.03802169, -0.03700922],
               [ 0.0598804 ,  0.02581887,  0.00509231]],
      
              [[ 0.01709368, -0.00630599,  0.01629886],
               [ 0.00920585,  0.00400731, -0.00266765],
               [-0.00658293,  0.0067501 , -0.01343034],
               ...,
               [ 0.00685193,  0.0055429 ,  0.00788099],
               [ 0.00275637,  0.00202491,  0.00451132],
               [-0.00382311, -0.00651726, -0.00863301]],
      
              [[ 0.00131005,  0.00396284,  0.00358667],
               [-0.02293317, -0.02470869, -0.02028217],
               [-0.00889773, -0.00958227, -0.01082166],
               ...,
               [ 0.00961991,  0.0088714 ,  0.00861739],
               [ 0.01251388,  0.0129503 ,  0.0111852 ],
               [-0.01122307, -0.00938066, -0.01037044]]]])

    • omega_global_stds
      (chain, draw, omega_global_stds_dim_0)
      float64
      2.027 0.3923 0.208 ... 3.015 1.214

      array([[[2.02687573, 0.3922567 , 0.20800552],
              [1.42338109, 1.39537257, 1.25244312],
              [0.17172083, 0.39997914, 0.46632279],
              ...,
              [0.49741775, 0.22137572, 0.42187734],
              [4.03165864, 2.1646064 , 0.14628529],
              [2.50023366, 3.0151032 , 1.21365994]]])

    • alpha_Chile
      (chain, draw, equations)
      float64
      -0.1192 -0.1203 ... -0.2583 -0.2283

      array([[[-0.11924555, -0.12032095, -0.10467121],
              [ 0.09605114,  0.04042802,  0.0695121 ],
              [ 0.19930289,  0.20740156,  0.2040223 ],
              ...,
              [ 0.16471413,  0.20172513,  0.06137248],
              [ 0.01225394,  0.08455854,  0.02188007],
              [-0.26668872, -0.25826539, -0.22825017]]])

    • betaX_South Africa
      (chain, draw, betaX_South Africa_dim_0, betaX_South Africa_dim_1)
      float64
      -0.05584 -0.04898 ... -0.01442

      array([[[[-0.0558436 , -0.04898187, -0.05355381],
               [-0.05030295, -0.04268354, -0.05209047],
               [-0.06362075, -0.05213718, -0.06295628],
               ...,
               [-0.00370569, -0.00070618, -0.00429591],
               [-0.00026378,  0.00221167, -0.00043544],
               [ 0.05821865,  0.05091112,  0.05731178]],
      
              [[-0.07427694, -0.06170692, -0.06658133],
               [-0.0638319 , -0.05446519, -0.05642085],
               [-0.0823938 , -0.07004981, -0.07096411],
               ...,
               [-0.00576356, -0.00474655, -0.00073715],
               [-0.00335177, -0.00192779,  0.00204938],
               [ 0.06017439,  0.05778677,  0.06944154]],
      
              [[ 0.04658698,  0.04616185,  0.04584471],
               [ 0.04232194,  0.04217134,  0.04243651],
               [ 0.05361996,  0.05414532,  0.05408819],
               ...,
      ...
               ...,
               [ 0.01480562, -0.00324349,  0.00864162],
               [ 0.02060229, -0.01014975,  0.00712865],
               [ 0.11584537,  0.01655988,  0.05265053]],
      
              [[ 0.01950713, -0.0092738 , -0.00900151],
               [ 0.0130672 , -0.00754261,  0.00406379],
               [ 0.01326231, -0.00838295, -0.00127099],
               ...,
               [-0.00235201,  0.00123899,  0.0012021 ],
               [-0.00255293,  0.00180714, -0.00168518],
               [-0.01246222,  0.01020893, -0.02097644]],
      
              [[ 0.01618206,  0.01837856,  0.01680204],
               [ 0.01429436,  0.01593231,  0.01433676],
               [ 0.01775231,  0.01968737,  0.01814331],
               ...,
               [ 0.0008452 ,  0.00034234,  0.00098735],
               [ 0.00027306, -0.00034906,  0.00054784],
               [-0.0154514 , -0.01924211, -0.01441864]]]])

    • noise_chol_Canada_stds
      (chain, draw, noise_chol_Canada_stds_dim_0)
      float64
      1.104 0.825 1.756 ... 0.5721 1.105

      array([[[1.10440523, 0.82503859, 1.75570064],
              [0.15839307, 1.82599118, 0.10349833],
              [0.1085844 , 2.45752976, 1.17689712],
              ...,
              [0.67556354, 3.84087625, 1.84996594],
              [3.21172324, 1.19995824, 1.50126291],
              [0.94243576, 0.5721334 , 1.10479856]]])

    • z_scale_beta_South Africa
      (chain, draw)
      float64
      0.1073 0.1805 ... 0.2544 0.2265

      array([[0.10725401, 0.18053172, 0.15312198, 0.13222558, 0.24763501,
              0.13829208, 0.13942574, 0.22536165, 0.0804554 , 0.16919095,
              0.09650668, 0.43661526, 0.11085958, 0.19899226, 0.08281941,
              0.07041651, 0.13845667, 0.23730792, 0.1101118 , 0.13838181,
              0.38630228, 0.1075834 , 0.17936368, 0.10454221, 0.09760238,
              0.19306042, 0.14542157, 0.15596088, 0.20652342, 0.51818893,
              0.09761156, 0.30728218, 0.0837425 , 0.35364186, 0.10977368,
              0.18523932, 0.32144508, 0.36644665, 0.33300565, 0.24270826,
              0.10655736, 0.21650779, 1.10851693, 0.19038574, 0.09248167,
              0.42827783, 0.25155635, 0.13940242, 0.21130247, 0.17644408,
              0.08264195, 0.28730601, 0.12524715, 0.54499077, 0.35556992,
              0.78320452, 0.36482641, 0.14980467, 0.19185827, 0.10402998,
              0.10465709, 0.13258314, 0.51721945, 0.12322392, 0.12148108,
              0.14556979, 0.10882881, 0.20944164, 0.07319728, 0.10113682,
              0.48365335, 0.28372294, 0.20965392, 0.14507687, 0.33385838,
              0.09031964, 0.35193183, 0.0726045 , 0.21016792, 0.13165753,
              0.62025143, 0.14487309, 0.18718442, 0.16994823, 0.10752624,
              0.20953533, 0.29508935, 0.15935652, 0.08113116, 0.36304941,
              0.17457381, 0.09257469, 0.20229817, 0.27807935, 0.25228236,
              0.47765986, 0.04043506, 0.17068503, 0.23606871, 0.21949982,
      ...
              0.25812428, 0.25584492, 0.12000788, 0.18615161, 0.30618276,
              0.55531509, 0.3798937 , 0.58517722, 1.33472023, 0.08258648,
              0.17049598, 0.13462352, 0.13251328, 0.3574387 , 0.16609369,
              0.17063956, 0.22181368, 0.31298038, 0.10275053, 0.05074391,
              0.14210875, 0.10690855, 0.23991028, 0.10684294, 0.34441436,
              0.29376056, 0.13149677, 0.18759748, 0.10411764, 0.36140611,
              0.08693992, 0.19647584, 0.20251634, 0.18216841, 0.15343795,
              0.09189746, 0.14098726, 0.40627829, 0.14786393, 0.38931897,
              0.17453446, 0.14334555, 0.10576873, 0.15494502, 0.1223162 ,
              0.44686162, 0.19276915, 0.22505745, 0.44672386, 0.06326841,
              0.15580757, 0.26850481, 0.1358556 , 0.13065448, 0.35651341,
              0.45386905, 0.1353396 , 0.23605247, 0.49807726, 0.1012356 ,
              0.22667477, 0.29198482, 0.3749364 , 1.06615042, 0.12785009,
              0.11832592, 0.12795421, 0.67197296, 0.1005462 , 0.23591892,
              0.1126967 , 1.15764445, 0.12701876, 0.27796705, 0.07589608,
              0.23126463, 0.10319304, 0.10209158, 0.13637707, 0.18236102,
              0.10418193, 0.2118901 , 0.16719501, 0.12298671, 0.29827216,
              0.27316018, 0.11454635, 0.43375971, 0.14775724, 0.16408741,
              0.23225362, 0.18957495, 0.15405318, 0.25925591, 0.10530855,
              0.08787894, 0.11283592, 0.27737801, 0.25435022, 0.22653212]])

    • alpha_hat_scale
      (chain, draw)
      float64
      0.0727 0.1192 ... 0.2113 0.1635

      array([[0.07269615, 0.11921829, 0.23143252, 0.84861949, 0.16966103,
              0.5075582 , 0.67664624, 0.20809928, 0.30311923, 0.64344922,
              1.01196531, 0.07163681, 0.14849358, 0.70496493, 0.71984082,
              0.09816693, 0.30453596, 0.16022729, 0.34023738, 0.18437594,
              0.08933639, 0.12849086, 0.10990283, 0.10864449, 0.39733202,
              0.22996314, 0.74297684, 0.09706945, 0.13139282, 0.11102822,
              0.14630976, 0.15336906, 0.56344578, 0.41766301, 0.52541364,
              0.26019061, 0.33760547, 0.19281295, 0.35854335, 0.07862992,
              0.1358479 , 0.43859383, 0.20273686, 0.13698435, 0.55731002,
              0.20756932, 0.3602051 , 0.06894599, 0.16491305, 0.24257593,
              0.09313312, 0.32056066, 0.19396391, 0.10980309, 0.24942448,
              0.10673777, 0.1348833 , 0.22183752, 0.19270976, 0.13682576,
              0.06966482, 0.24358429, 0.16095191, 0.27298288, 0.19911166,
              0.20125226, 0.16671434, 0.09073042, 0.2481739 , 0.10550495,
              0.04841081, 4.4755525 , 0.10680349, 0.37361509, 0.08602964,
              0.06953387, 0.13064071, 0.32415379, 0.39946363, 0.15933561,
              0.31391744, 0.11403867, 0.11453116, 0.31961843, 0.22937366,
              0.38438506, 0.12169275, 0.16522245, 0.45366146, 0.4183631 ,
              0.28288921, 0.11183029, 0.0706044 , 0.09158592, 0.35316383,
              0.21230669, 0.18942057, 0.10234242, 0.23640088, 0.34122672,
      ...
              0.11510218, 0.28715445, 0.06325536, 0.2182641 , 0.05826435,
              0.23779747, 0.12024905, 0.20812626, 0.08283591, 0.12346339,
              0.12013893, 0.14929195, 0.20226776, 0.07193751, 0.21939499,
              0.10643118, 0.16011808, 0.2110086 , 0.14463812, 0.14317078,
              0.64361059, 0.1397251 , 0.46588068, 0.12380565, 0.11512193,
              0.0764919 , 0.16231359, 0.07582565, 0.12714337, 0.13839952,
              0.19057452, 0.19415788, 0.05211183, 0.19719842, 0.24943753,
              0.19734745, 0.29850262, 0.34822184, 0.51842222, 0.07572321,
              0.16820925, 0.20390044, 0.28380267, 0.07146765, 0.06384731,
              0.28055985, 0.09380778, 0.4739377 , 0.3139601 , 0.12539639,
              0.1713179 , 0.15938139, 0.14701943, 0.1486747 , 0.33452924,
              0.31705784, 0.42520577, 0.19829761, 0.16739522, 0.17925151,
              0.25676685, 0.33851669, 1.13426024, 0.2406065 , 0.15675693,
              0.11306248, 0.24601556, 0.14152391, 0.16138818, 0.1007528 ,
              0.21083613, 0.21538297, 0.23693717, 0.34581154, 0.46284469,
              0.20132751, 0.62907934, 0.67779712, 0.89761045, 0.30522743,
              0.35975874, 0.27838732, 0.29728314, 0.10639236, 0.09146294,
              0.36255709, 0.32174608, 0.07658706, 0.17405355, 0.09338064,
              0.62281929, 0.2122815 , 0.23269755, 0.15123917, 0.37040656,
              0.21158872, 0.31484035, 0.28298487, 0.21128568, 0.16345312]])

    • z_scale_alpha_Chile
      (chain, draw)
      float64
      0.1228 0.1802 ... 0.1581 0.1447

      array([[0.12280496, 0.1801886 , 0.06214498, 0.9396314 , 0.29532813,
              0.14485331, 0.25391981, 0.09722508, 0.84281462, 0.1754833 ,
              0.14833856, 0.16231669, 0.25938678, 0.80888171, 1.90351011,
              0.36425559, 0.18082723, 0.14113397, 0.76681855, 0.28962159,
              0.33811589, 0.20426871, 0.15037805, 0.11512526, 0.3217111 ,
              0.42380128, 0.13099404, 0.66522252, 0.10802987, 0.12609351,
              0.08573739, 0.25037987, 0.15922931, 0.30542747, 0.19328752,
              0.1186681 , 0.16841963, 0.14580037, 0.57867261, 1.36610174,
              0.09644918, 0.07780445, 0.17635274, 0.06792031, 0.60318196,
              0.26870654, 0.20632756, 0.22098476, 0.30685076, 0.1174546 ,
              0.10842272, 0.63121043, 0.13528979, 0.12295001, 0.21622103,
              0.32004973, 0.20743825, 0.12341796, 0.16046552, 0.12204894,
              0.15700979, 0.47426836, 0.59871361, 0.130174  , 0.17841922,
              0.05130847, 0.24402754, 0.26311468, 0.3673745 , 0.21245848,
              0.15455659, 0.16135878, 0.22060327, 0.08259884, 0.20288021,
              0.19934387, 0.4310693 , 0.15725011, 0.11558767, 0.18058161,
              0.40076971, 1.59883351, 0.13512574, 0.07111749, 0.2259875 ,
              0.11708975, 0.17962592, 0.20554337, 0.10674949, 0.38846715,
              0.24648182, 0.26746079, 0.21472927, 0.58726211, 0.2480894 ,
              0.22786661, 0.07168677, 0.15040255, 0.31669026, 0.81533274,
      ...
              0.10732727, 0.25540907, 0.18845381, 0.18159762, 0.84641552,
              0.95657691, 0.29089986, 0.10297957, 2.18222589, 0.18367526,
              0.13414844, 0.27980592, 0.16258218, 0.22178631, 0.24193235,
              0.33693783, 0.15629178, 0.13617769, 0.15148151, 0.17607153,
              0.13714411, 0.11630865, 0.50907849, 0.18781747, 0.25961083,
              0.17828212, 0.30363962, 0.24837124, 0.28097205, 0.1212715 ,
              0.15934898, 0.17463097, 0.36715658, 0.1965841 , 0.15911579,
              0.18945764, 0.53008639, 1.60310381, 0.29878552, 0.31898287,
              0.2580223 , 0.16231215, 0.25781832, 0.12833553, 0.22224723,
              0.11660717, 0.11259463, 0.70996616, 0.26725195, 0.27916963,
              0.0648474 , 0.13238682, 0.14569057, 0.08504128, 0.34093376,
              0.0886281 , 0.41900118, 0.14394318, 0.06623067, 0.07323047,
              0.1616256 , 0.1730078 , 0.29926958, 0.41316745, 0.48462346,
              0.06349766, 1.03391098, 0.09250841, 0.35071748, 0.11720248,
              0.22021422, 0.25051871, 0.07971699, 0.11641528, 0.15521057,
              0.44110744, 0.19682487, 0.18227832, 0.16280956, 0.16616888,
              0.25973939, 0.12016903, 0.20314555, 0.14937808, 0.44411365,
              0.35396291, 0.30764843, 0.41954436, 0.29483912, 0.20793049,
              0.5363871 , 0.08154625, 0.31168436, 0.15164051, 0.20415209,
              0.14594542, 0.26251029, 0.31846204, 0.15811698, 0.1447256 ]])

    • z_scale_alpha_United Kingdom
      (chain, draw)
      float64
      0.1462 0.2181 ... 0.1132 0.1805

      array([[0.14615347, 0.21814529, 0.08921965, 0.15732618, 0.10877408,
              0.26838932, 0.23372908, 0.10478102, 0.30007749, 0.20797412,
              0.24297004, 0.14059216, 0.50656317, 0.04252637, 0.42111484,
              0.16856053, 0.1426295 , 0.13709904, 0.44633171, 0.92469999,
              0.27874396, 0.96112713, 0.55251534, 0.15682131, 0.58532478,
              0.0775758 , 0.31647196, 0.10230881, 0.09274098, 0.17951364,
              0.10385349, 0.34649954, 0.1111455 , 0.15686222, 0.10405297,
              0.14926344, 0.1219439 , 0.1299249 , 0.70901532, 0.1017012 ,
              0.09479976, 0.30732467, 0.22215443, 0.25663154, 0.09132576,
              0.11221097, 0.20059669, 0.08295577, 0.619365  , 0.17270199,
              0.11771648, 0.1574121 , 0.1192092 , 0.19272859, 0.59577432,
              0.25757943, 0.30501459, 0.10930594, 0.32325162, 0.08842916,
              0.4478156 , 0.17351546, 0.47777777, 0.18264043, 0.18286935,
              0.14669802, 0.18226189, 0.18756594, 0.8562476 , 0.12543233,
              0.17217142, 0.06201229, 0.18986327, 0.15523575, 0.26112021,
              0.85582229, 0.29504765, 0.08046924, 0.14008726, 0.14362572,
              0.11293334, 0.14019856, 0.20855488, 0.33438951, 0.33480502,
              0.20368539, 0.19183289, 0.07625658, 0.3757983 , 0.13890529,
              0.3200278 , 0.13286024, 0.08474757, 0.06918901, 0.82314137,
              0.13584292, 0.19353441, 0.44884621, 0.20077177, 0.31292323,
      ...
              0.27453994, 0.2341724 , 0.05568105, 0.18127981, 0.17273249,
              0.73311412, 1.24177591, 0.11517602, 0.20825295, 0.22007299,
              0.1253171 , 0.49008584, 0.08482854, 0.37319298, 0.3061145 ,
              0.18899357, 0.20976727, 0.2296741 , 0.09501514, 0.24112746,
              0.09570809, 0.18475431, 0.16895616, 0.15710433, 0.52212712,
              0.47383848, 0.13838211, 0.21483669, 0.07641952, 0.28699865,
              0.26494069, 0.07559187, 0.09959629, 0.23535023, 0.23532044,
              0.09781274, 0.30847832, 0.06363466, 0.18676587, 0.16781683,
              0.18327309, 0.06711008, 0.48003086, 0.09125349, 0.23476454,
              0.10241234, 0.78334824, 0.06992242, 0.27470254, 0.13828056,
              0.17578395, 0.15507622, 0.1191825 , 0.11911828, 0.17926634,
              0.24485954, 0.11456693, 0.43582202, 0.14602728, 0.46181792,
              0.14520694, 0.42904162, 0.06024894, 0.24232622, 0.13150011,
              0.09110117, 0.12624898, 0.21179786, 0.5072583 , 0.30542341,
              0.15424995, 0.26049769, 0.35399283, 0.14698489, 0.25859346,
              0.15470331, 0.20398941, 0.13981706, 0.32678196, 0.12441435,
              0.46566708, 0.0994699 , 0.36349282, 0.19693197, 0.05707575,
              0.1943626 , 0.24143071, 0.29668235, 0.22333971, 0.13946168,
              0.20708734, 0.19571303, 0.2096319 , 0.08398149, 0.09573948,
              0.1769644 , 0.46251936, 0.19525321, 0.1131867 , 0.18048441]])

    • noise_chol_New Zealand_corr
      (chain, draw, noise_chol_New Zealand_corr_dim_0, noise_chol_New Zealand_corr_dim_1)
      float64
      1.0 0.3852 0.2603 ... -0.1005 1.0

      array([[[[ 1.        ,  0.38524886,  0.26031599],
               [ 0.38524886,  1.        , -0.16907472],
               [ 0.26031599, -0.16907472,  1.        ]],
      
              [[ 1.        ,  0.14718378, -0.71368448],
               [ 0.14718378,  1.        , -0.03434326],
               [-0.71368448, -0.03434326,  1.        ]],
      
              [[ 1.        ,  0.03681494,  0.04966948],
               [ 0.03681494,  1.        , -0.30363802],
               [ 0.04966948, -0.30363802,  1.        ]],
      
              ...,
      
              [[ 1.        , -0.21527001, -0.38740003],
               [-0.21527001,  1.        ,  0.14113665],
               [-0.38740003,  0.14113665,  1.        ]],
      
              [[ 1.        ,  0.08716486,  0.27606965],
               [ 0.08716486,  1.        , -0.15615154],
               [ 0.27606965, -0.15615154,  1.        ]],
      
              [[ 1.        , -0.07402657,  0.02915884],
               [-0.07402657,  1.        , -0.10050008],
               [ 0.02915884, -0.10050008,  1.        ]]]])

    • noise_chol_United States_corr
      (chain, draw, noise_chol_United States_corr_dim_0, noise_chol_United States_corr_dim_1)
      float64
      1.0 0.01808 -0.07775 ... 0.2051 1.0

      array([[[[ 1.        ,  0.01807806, -0.07774922],
               [ 0.01807806,  1.        ,  0.40628986],
               [-0.07774922,  0.40628986,  1.        ]],
      
              [[ 1.        , -0.04725293,  0.14554113],
               [-0.04725293,  1.        ,  0.28012288],
               [ 0.14554113,  0.28012288,  1.        ]],
      
              [[ 1.        , -0.18640816,  0.03443714],
               [-0.18640816,  1.        ,  0.46879452],
               [ 0.03443714,  0.46879452,  1.        ]],
      
              ...,
      
              [[ 1.        , -0.01840045, -0.38639318],
               [-0.01840045,  1.        ,  0.03570362],
               [-0.38639318,  0.03570362,  1.        ]],
      
              [[ 1.        , -0.05084678, -0.05729962],
               [-0.05084678,  1.        ,  0.04874449],
               [-0.05729962,  0.04874449,  1.        ]],
      
              [[ 1.        ,  0.35721589, -0.27867325],
               [ 0.35721589,  1.        ,  0.20505815],
               [-0.27867325,  0.20505815,  1.        ]]]])

    • noise_chol_Chile
      (chain, draw, noise_chol_Chile_dim_0)
      float64
      0.02867 -0.06896 ... -0.1446 0.3575

      array([[[ 2.86658712e-02, -6.89626277e-02,  3.97577024e-01,
                1.24975708e-01,  2.03544014e-01,  8.05828265e-01],
              [ 1.96448849e-01, -1.67392731e-01,  3.91707574e-01,
                1.05598630e-01,  1.11264155e-02,  4.23233769e-01],
              [ 4.93996180e+00, -2.28576964e-02,  7.06186371e-01,
                8.99573106e-01,  1.07460087e-01,  2.23196130e+00],
              ...,
              [ 3.05380895e-03, -8.90622680e-01,  3.41536594e+00,
               -7.56755854e-02, -1.92021092e-03,  2.06858270e-01],
              [ 1.79712235e-01,  3.31228560e-01,  1.04084437e+00,
                3.82925750e-01,  3.85452013e-01,  1.53265523e+00],
              [ 3.08303752e-01, -4.39043564e-01,  1.56148763e+00,
                2.08548661e-02, -1.44607107e-01,  3.57477207e-01]]])

    • z_scale_alpha_United States
      (chain, draw)
      float64
      0.2131 0.2173 ... 0.9523 0.2111

      array([[0.213131  , 0.21725718, 0.22404577, 0.25395186, 1.25995739,
              0.05129905, 0.28177037, 0.49832128, 0.55824947, 0.27270416,
              0.54184521, 0.23547635, 0.1661448 , 0.1095501 , 0.09859127,
              0.38130638, 0.13448592, 0.19701676, 0.28648084, 0.17895608,
              0.12634376, 0.43515596, 0.13119484, 0.93350449, 0.20318491,
              0.27020998, 0.12537416, 0.06455312, 0.25969604, 0.19505406,
              0.13752629, 0.11508442, 0.69842961, 0.63597102, 0.08573165,
              0.15040056, 0.07971116, 0.27761443, 0.29080742, 0.10751002,
              0.16730017, 0.22935299, 0.18744526, 0.16046437, 0.09227502,
              0.08299103, 0.14732107, 0.18676536, 1.44512843, 0.09468049,
              0.36356497, 0.47477523, 0.10161336, 0.2142195 , 0.2393077 ,
              0.21300733, 0.06310802, 0.17393768, 0.12666332, 0.11760015,
              0.26429748, 0.33236386, 0.39800096, 0.08165497, 0.1144731 ,
              0.08405083, 0.12684565, 0.16087119, 0.1557723 , 0.27829468,
              0.10828135, 0.30089728, 0.1192222 , 0.08841513, 0.17681336,
              0.2129509 , 0.08544167, 0.09566903, 0.4035193 , 0.65962495,
              0.24762694, 0.17419881, 0.39933495, 0.48364864, 0.24012817,
              0.20604128, 0.3841842 , 0.15346105, 0.1078102 , 0.23174745,
              0.74321902, 0.16599125, 0.49158993, 0.10894033, 0.29102026,
              0.15326786, 0.10167379, 0.14005689, 0.23751325, 0.78210725,
      ...
              0.14312609, 0.14504121, 0.12848571, 0.09837204, 0.15276736,
              0.63350922, 0.07001615, 0.16307457, 0.23126341, 0.19017895,
              0.18095649, 0.31685085, 0.36320904, 0.20086189, 0.09804208,
              0.11229264, 0.15529835, 0.10684901, 0.16513884, 1.00334368,
              0.90216595, 0.25810317, 1.45173001, 0.83503671, 0.10299706,
              0.20407598, 0.04759074, 0.10313566, 0.3615443 , 0.40750234,
              0.12881712, 0.29223599, 0.39753163, 0.6605557 , 0.50994988,
              0.14554548, 0.13850693, 0.67496332, 0.23446763, 0.1438275 ,
              0.10050025, 0.22235178, 0.35316296, 0.11539015, 0.08959966,
              0.19899996, 0.07770607, 0.12859195, 0.11907838, 0.19230079,
              0.15656008, 0.12932708, 0.29257899, 0.21465011, 0.39832942,
              0.04844192, 0.07065745, 0.15464813, 0.16818291, 0.13314731,
              0.06698879, 0.37597655, 0.15014681, 0.10834985, 0.32433376,
              0.12216928, 0.50987548, 1.23717434, 0.09642178, 0.37018357,
              0.18213376, 0.05193194, 0.1497674 , 0.22702825, 0.24786638,
              0.05947143, 0.17178903, 0.29558854, 0.25410012, 0.30833692,
              0.15885424, 0.11080126, 0.24733362, 0.2618624 , 0.10312871,
              0.20318639, 0.12534367, 0.2954155 , 0.1974756 , 0.13267557,
              0.26437944, 0.26765847, 0.09003416, 0.28084225, 0.6000107 ,
              0.15638529, 0.1348397 , 0.114784  , 0.95225872, 0.2111357 ]])

    • noise_chol_Ireland_stds
      (chain, draw, noise_chol_Ireland_stds_dim_0)
      float64
      3.052 2.263 0.1821 ... 0.4276 0.554

      array([[[3.05179578, 2.26286263, 0.18210023],
              [0.6475452 , 0.77795524, 0.14694366],
              [0.7076372 , 2.20870574, 0.47444224],
              ...,
              [1.20541287, 1.17459754, 2.70575139],
              [1.56463364, 0.61174262, 1.03820005],
              [1.21394237, 0.4276016 , 0.55400795]]])

    • beta_hat_location
      (chain, draw)
      float64
      -0.1648 -0.2081 ... 0.0113 0.05914

      array([[-0.16481175, -0.20809496,  0.16284455, -0.06670417,  0.20153212,
               0.00238363,  0.06199665, -0.03543655, -0.03926312,  0.13693163,
               0.13141081,  0.10801654,  0.11110207, -0.10641381, -0.04353907,
               0.1056492 ,  0.06787589, -0.10119827, -0.04913159,  0.0462559 ,
              -0.23254297,  0.07203862, -0.1765229 ,  0.09002237, -0.08303859,
               0.05352949,  0.11311501,  0.11669136,  0.07052244, -0.0111081 ,
              -0.20942819,  0.13809954, -0.01091662,  0.01813257,  0.02249916,
               0.17290654,  0.00451771, -0.04546065,  0.1887338 ,  0.15981393,
              -0.12068138,  0.12706804, -0.10485724,  0.05808422,  0.1083918 ,
               0.11740385, -0.23974765,  0.01047011, -0.07072351,  0.02013301,
              -0.03522476, -0.09390172, -0.08729993, -0.02633896, -0.17301583,
              -0.16426084,  0.05181323,  0.02842454, -0.00801742, -0.09094017,
               0.05193375, -0.12707409,  0.01230593, -0.00335992, -0.07555674,
              -0.10280913, -0.16115713,  0.18664087,  0.31247593,  0.1037974 ,
              -0.02645771,  0.07510285,  0.01774999, -0.03879357, -0.18341457,
              -0.01466648,  0.03587112, -0.07496613,  0.292636  , -0.28021826,
               0.13067678,  0.02094223, -0.11146711, -0.08585967, -0.12881305,
               0.02642538,  0.15162453, -0.12306617, -0.02078033, -0.05134788,
              -0.02570612,  0.09287529,  0.14307387,  0.07750462, -0.08578185,
              -0.00848868,  0.02153072,  0.09048901, -0.09708856,  0.16906214,
      ...
               0.15142473, -0.32155753,  0.03281664, -0.12321917, -0.05759783,
               0.19264854,  0.0715562 , -0.02225798,  0.00513071,  0.01819049,
               0.08043267, -0.10933417,  0.01239515,  0.00716248, -0.02060367,
              -0.14038532,  0.17588652,  0.04889748, -0.04151308, -0.0464201 ,
              -0.09352181,  0.06807259,  0.00763478, -0.08002759, -0.04640006,
              -0.11200583,  0.09651522,  0.17205287,  0.07632241,  0.05538552,
              -0.04992605, -0.03717167, -0.10774248,  0.07257829, -0.16353298,
               0.02617405,  0.10574109,  0.07088435, -0.16879805, -0.08567799,
               0.03575711,  0.20419767, -0.02997488, -0.09988271, -0.06459231,
              -0.22554068,  0.04772152, -0.19766586,  0.080018  , -0.09377091,
              -0.05714076, -0.01117028, -0.12294586, -0.1362682 , -0.06380633,
               0.04973399, -0.12680432,  0.04301216, -0.03454063,  0.19510736,
              -0.25272959, -0.00048978, -0.0808569 , -0.16610265, -0.01780281,
              -0.10247105,  0.05562454,  0.01445049, -0.20653719,  0.14408886,
              -0.03978285,  0.02297927, -0.18641727, -0.01959715, -0.15556193,
              -0.0172424 , -0.00495404,  0.05588277,  0.17457213, -0.01759205,
              -0.053386  ,  0.1278743 , -0.00732395,  0.09852238, -0.00235284,
               0.00120081,  0.116359  ,  0.00593622, -0.11993341, -0.06500739,
               0.15256744,  0.01469552, -0.08728158,  0.12287521, -0.10911156,
               0.01910623, -0.16061979, -0.18130079,  0.01129778,  0.05913939]])

    • rho
      (chain, draw)
      float64
      0.4541 0.6935 ... 0.1761 0.5731

      array([[0.45408371, 0.69350899, 0.35049896, 0.23006247, 0.76242918,
              0.70501677, 0.05367603, 0.67104457, 0.27539228, 0.7166245 ,
              0.45334409, 0.84363359, 0.35948475, 0.03437022, 0.19584551,
              0.42114371, 0.4940945 , 0.67276139, 0.84154138, 0.2502528 ,
              0.79031196, 0.48646038, 0.76934743, 0.91227126, 0.67111831,
              0.2401683 , 0.52495365, 0.51705828, 0.14105183, 0.73161832,
              0.8221039 , 0.20932337, 0.28994766, 0.24748005, 0.53707395,
              0.33366829, 0.69892448, 0.50569658, 0.83425951, 0.34720364,
              0.57428598, 0.17666474, 0.8467154 , 0.87396205, 0.29832267,
              0.3786298 , 0.50826547, 0.37942305, 0.62288707, 0.50273959,
              0.49671072, 0.32090275, 0.51230094, 0.43734976, 0.51710441,
              0.62698532, 0.55284996, 0.54306173, 0.46399675, 0.73824307,
              0.35566467, 0.1523995 , 0.26756316, 0.70418041, 0.52058539,
              0.39748723, 0.93960598, 0.58849021, 0.87406193, 0.88156013,
              0.62846781, 0.29445907, 0.06498372, 0.67313392, 0.79593263,
              0.96395349, 0.17048755, 0.35716337, 0.51502277, 0.43679723,
              0.12226093, 0.46175202, 0.3580057 , 0.19219847, 0.57047203,
              0.52972452, 0.07763128, 0.29154291, 0.23669705, 0.19362827,
              0.66743246, 0.42616666, 0.2766233 , 0.60863324, 0.26673162,
              0.85178987, 0.75493282, 0.52312087, 0.15625225, 0.86869569,
      ...
              0.5916496 , 0.95019525, 0.66363723, 0.60389902, 0.42312456,
              0.65388926, 0.41973304, 0.78954301, 0.67610768, 0.49357635,
              0.94811528, 0.1627281 , 0.81540546, 0.71591941, 0.15847906,
              0.42608947, 0.59020144, 0.60466001, 0.16386533, 0.6563939 ,
              0.72368189, 0.71268739, 0.08435803, 0.16813328, 0.71776272,
              0.47468738, 0.33987693, 0.51241451, 0.53359411, 0.7615783 ,
              0.22030355, 0.69281104, 0.41457362, 0.31889544, 0.59163158,
              0.41498785, 0.50451057, 0.47400243, 0.69923042, 0.27328454,
              0.73617488, 0.59073884, 0.67845796, 0.236538  , 0.19893683,
              0.19526877, 0.86770475, 0.70382729, 0.58445592, 0.6208028 ,
              0.7915242 , 0.82593155, 0.4962333 , 0.70547759, 0.80282085,
              0.11878151, 0.19505328, 0.64237388, 0.68187787, 0.61570776,
              0.93888417, 0.22076176, 0.43904963, 0.47437682, 0.47768572,
              0.73397547, 0.64809938, 0.28300901, 0.41784012, 0.39098325,
              0.49852955, 0.66886414, 0.71536127, 0.18841023, 0.2009872 ,
              0.50540092, 0.43635371, 0.32098071, 0.26902961, 0.38409436,
              0.1486014 , 0.75615635, 0.51535178, 0.43578111, 0.32947848,
              0.19946403, 0.1354591 , 0.74983673, 0.91626011, 0.24296797,
              0.14304216, 0.21893295, 0.47244829, 0.20654953, 0.55832374,
              0.64679508, 0.33490577, 0.42673137, 0.17605767, 0.57305957]])

    • z_scale_alpha_Canada
      (chain, draw)
      float64
      0.06378 0.2621 ... 0.06267 0.2395

      array([[0.06378199, 0.26213638, 0.10562488, 0.41412078, 0.22852257,
              0.97315592, 0.1018424 , 0.28849668, 0.31188091, 0.16670602,
              0.19405259, 0.15868021, 0.14469301, 0.34340057, 0.23637804,
              0.11256724, 0.63783365, 0.0999994 , 0.1261458 , 0.34533882,
              0.06299829, 0.10649731, 0.31179513, 0.13521697, 0.15208259,
              0.16434184, 0.13069923, 0.15646203, 0.25548276, 0.17661368,
              0.23370614, 0.25636507, 0.13942621, 0.39854945, 0.13636833,
              0.10310414, 0.39128064, 0.12635791, 0.22949415, 0.23036678,
              0.12051084, 0.10650911, 0.12005857, 0.46443176, 3.7093797 ,
              0.12245853, 0.10306819, 1.55604689, 0.06856524, 0.08798214,
              0.13534854, 0.14941395, 0.15001066, 0.1209059 , 0.10413524,
              0.1032491 , 0.20396899, 0.31495513, 0.11535401, 0.35148579,
              0.18075366, 0.19389029, 0.08548038, 0.15217848, 0.19976525,
              0.20243536, 0.25413403, 0.72784895, 0.20917203, 0.13343318,
              0.08898976, 0.23062395, 0.27564811, 0.34233545, 0.18439108,
              0.26244743, 0.07358966, 0.07545393, 0.58289477, 0.32524163,
              0.07374368, 0.18442543, 0.12958636, 0.2696356 , 0.18756169,
              0.11827149, 0.33316798, 0.15683388, 0.05593736, 0.1856784 ,
              0.19879242, 0.22442752, 0.23856679, 0.22624447, 0.11213538,
              0.12026965, 0.25985264, 0.50055825, 0.13438282, 0.20595772,
      ...
              0.08248672, 0.72677529, 0.80857457, 0.20586513, 0.47596947,
              0.15769514, 0.08850205, 0.16083444, 0.07485606, 0.07304545,
              0.18594709, 0.0954647 , 2.51901922, 0.1055115 , 0.10995192,
              0.54821221, 0.3098678 , 0.84624647, 0.16265487, 0.19637961,
              0.10971489, 0.15174734, 0.20759024, 0.13325213, 0.49380788,
              0.13177068, 0.18697702, 0.16572793, 0.49853711, 0.24387162,
              0.23964506, 0.19749614, 0.70791164, 0.15848289, 0.27759852,
              0.19001998, 0.26131136, 0.21886743, 0.10997396, 0.24131981,
              0.11431693, 0.11110756, 0.6115091 , 0.08767059, 0.23483956,
              0.19086222, 0.10834805, 0.10833937, 0.13314133, 0.27010614,
              0.08072827, 0.1878972 , 0.2072152 , 0.19607113, 0.31546982,
              0.29895169, 0.21528694, 0.07094348, 0.16626419, 0.23719245,
              0.1359794 , 0.13518073, 0.30263685, 0.06922079, 0.57380417,
              0.46551093, 0.23889615, 0.364586  , 0.23034022, 0.10063996,
              0.12269451, 0.25981145, 0.3079617 , 0.37582332, 0.13643984,
              0.31780538, 0.29426745, 0.14108259, 0.10929791, 0.57187571,
              0.23080312, 0.12899524, 0.21813754, 0.25141642, 0.07688701,
              0.14417158, 0.12121741, 0.33565333, 0.14715947, 0.10673218,
              0.09397568, 0.14081268, 0.44149728, 0.06293998, 0.10423666,
              0.14709606, 0.18111538, 0.17217239, 0.0626725 , 0.2394876 ]])

  • Indexes: (73)
    • chain
      PandasIndex

      PandasIndex(Int64Index([0], dtype='int64', name='chain'))

    • draw
      PandasIndex

      PandasIndex(Int64Index([  0,   1,   2,   3,   4,   5,   6,   7,   8,   9,
                  ...
                  490, 491, 492, 493, 494, 495, 496, 497, 498, 499],
                 dtype='int64', name='draw', length=500))

    • omega_global_dim_0
      PandasIndex

      PandasIndex(Int64Index([0, 1, 2, 3, 4, 5], dtype='int64', name='omega_global_dim_0'))

    • betaX_Canada_dim_0
      PandasIndex

      PandasIndex(Int64Index([0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18,
                  19, 20, 21],
                 dtype='int64', name='betaX_Canada_dim_0'))

    • betaX_Canada_dim_1
      PandasIndex

      PandasIndex(Int64Index([0, 1, 2], dtype='int64', name='betaX_Canada_dim_1'))

    • noise_chol_South Africa_dim_0
      PandasIndex

      PandasIndex(Int64Index([0, 1, 2, 3, 4, 5], dtype='int64', name='noise_chol_South Africa_dim_0'))

    • omega_New Zealand_dim_0
      PandasIndex

      PandasIndex(Int64Index([0, 1, 2], dtype='int64', name='omega_New Zealand_dim_0'))

    • omega_New Zealand_dim_1
      PandasIndex

      PandasIndex(Int64Index([0, 1, 2], dtype='int64', name='omega_New Zealand_dim_1'))

    • equations
      PandasIndex

      PandasIndex(Index(['dl_gdp', 'dl_cons', 'dl_gfcf'], dtype='object', name='equations'))

    • lags
      PandasIndex

      PandasIndex(Int64Index([1, 2], dtype='int64', name='lags'))

    • cross_vars
      PandasIndex

      PandasIndex(Index(['dl_gdp', 'dl_cons', 'dl_gfcf'], dtype='object', name='cross_vars'))

    • betaX_United States_dim_0
      PandasIndex

      PandasIndex(Int64Index([ 0,  1,  2,  3,  4,  5,  6,  7,  8,  9, 10, 11, 12, 13, 14, 15, 16,
                  17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33,
                  34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45],
                 dtype='int64', name='betaX_United States_dim_0'))

    • betaX_United States_dim_1
      PandasIndex

      PandasIndex(Int64Index([0, 1, 2], dtype='int64', name='betaX_United States_dim_1'))

    • noise_chol_United Kingdom_stds_dim_0
      PandasIndex

      PandasIndex(Int64Index([0, 1, 2], dtype='int64', name='noise_chol_United Kingdom_stds_dim_0'))

    • noise_chol_New Zealand_stds_dim_0
      PandasIndex

      PandasIndex(Int64Index([0, 1, 2], dtype='int64', name='noise_chol_New Zealand_stds_dim_0'))

    • omega_United Kingdom_dim_0
      PandasIndex

      PandasIndex(Int64Index([0, 1, 2], dtype='int64', name='omega_United Kingdom_dim_0'))

    • omega_United Kingdom_dim_1
      PandasIndex

      PandasIndex(Int64Index([0, 1, 2], dtype='int64', name='omega_United Kingdom_dim_1'))

    • omega_Australia_dim_0
      PandasIndex

      PandasIndex(Int64Index([0, 1, 2], dtype='int64', name='omega_Australia_dim_0'))

    • omega_Australia_dim_1
      PandasIndex

      PandasIndex(Int64Index([0, 1, 2], dtype='int64', name='omega_Australia_dim_1'))

    • noise_chol_South Africa_stds_dim_0
      PandasIndex

      PandasIndex(Int64Index([0, 1, 2], dtype='int64', name='noise_chol_South Africa_stds_dim_0'))

    • omega_Ireland_dim_0
      PandasIndex

      PandasIndex(Int64Index([0, 1, 2], dtype='int64', name='omega_Ireland_dim_0'))

    • omega_Ireland_dim_1
      PandasIndex

      PandasIndex(Int64Index([0, 1, 2], dtype='int64', name='omega_Ireland_dim_1'))

    • noise_chol_Chile_corr_dim_0
      PandasIndex

      PandasIndex(Int64Index([0, 1, 2], dtype='int64', name='noise_chol_Chile_corr_dim_0'))

    • noise_chol_Chile_corr_dim_1
      PandasIndex

      PandasIndex(Int64Index([0, 1, 2], dtype='int64', name='noise_chol_Chile_corr_dim_1'))

    • noise_chol_United States_stds_dim_0
      PandasIndex

      PandasIndex(Int64Index([0, 1, 2], dtype='int64', name='noise_chol_United States_stds_dim_0'))

    • omega_United States_dim_0
      PandasIndex

      PandasIndex(Int64Index([0, 1, 2], dtype='int64', name='omega_United States_dim_0'))

    • omega_United States_dim_1
      PandasIndex

      PandasIndex(Int64Index([0, 1, 2], dtype='int64', name='omega_United States_dim_1'))

    • noise_chol_New Zealand_dim_0
      PandasIndex

      PandasIndex(Int64Index([0, 1, 2, 3, 4, 5], dtype='int64', name='noise_chol_New Zealand_dim_0'))

    • omega_Chile_dim_0
      PandasIndex

      PandasIndex(Int64Index([0, 1, 2], dtype='int64', name='omega_Chile_dim_0'))

    • omega_Chile_dim_1
      PandasIndex

      PandasIndex(Int64Index([0, 1, 2], dtype='int64', name='omega_Chile_dim_1'))

    • noise_chol_United States_dim_0
      PandasIndex

      PandasIndex(Int64Index([0, 1, 2, 3, 4, 5], dtype='int64', name='noise_chol_United States_dim_0'))

    • noise_chol_United Kingdom_corr_dim_0
      PandasIndex

      PandasIndex(Int64Index([0, 1, 2], dtype='int64', name='noise_chol_United Kingdom_corr_dim_0'))

    • noise_chol_United Kingdom_corr_dim_1
      PandasIndex

      PandasIndex(Int64Index([0, 1, 2], dtype='int64', name='noise_chol_United Kingdom_corr_dim_1'))

    • betaX_United Kingdom_dim_0
      PandasIndex

      PandasIndex(Int64Index([ 0,  1,  2,  3,  4,  5,  6,  7,  8,  9, 10, 11, 12, 13, 14, 15, 16,
                  17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33,
                  34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48],
                 dtype='int64', name='betaX_United Kingdom_dim_0'))

    • betaX_United Kingdom_dim_1
      PandasIndex

      PandasIndex(Int64Index([0, 1, 2], dtype='int64', name='betaX_United Kingdom_dim_1'))

    • betaX_Ireland_dim_0
      PandasIndex

      PandasIndex(Int64Index([ 0,  1,  2,  3,  4,  5,  6,  7,  8,  9, 10, 11, 12, 13, 14, 15, 16,
                  17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33,
                  34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48],
                 dtype='int64', name='betaX_Ireland_dim_0'))

    • betaX_Ireland_dim_1
      PandasIndex

      PandasIndex(Int64Index([0, 1, 2], dtype='int64', name='betaX_Ireland_dim_1'))

    • omega_South Africa_dim_0
      PandasIndex

      PandasIndex(Int64Index([0, 1, 2], dtype='int64', name='omega_South Africa_dim_0'))

    • omega_South Africa_dim_1
      PandasIndex

      PandasIndex(Int64Index([0, 1, 2], dtype='int64', name='omega_South Africa_dim_1'))

    • noise_chol_Canada_dim_0
      PandasIndex

      PandasIndex(Int64Index([0, 1, 2, 3, 4, 5], dtype='int64', name='noise_chol_Canada_dim_0'))

    • omega_global_corr_dim_0
      PandasIndex

      PandasIndex(Int64Index([0, 1, 2], dtype='int64', name='omega_global_corr_dim_0'))

    • omega_global_corr_dim_1
      PandasIndex

      PandasIndex(Int64Index([0, 1, 2], dtype='int64', name='omega_global_corr_dim_1'))

    • betaX_Australia_dim_0
      PandasIndex

      PandasIndex(Int64Index([ 0,  1,  2,  3,  4,  5,  6,  7,  8,  9, 10, 11, 12, 13, 14, 15, 16,
                  17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33,
                  34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48],
                 dtype='int64', name='betaX_Australia_dim_0'))

    • betaX_Australia_dim_1
      PandasIndex

      PandasIndex(Int64Index([0, 1, 2], dtype='int64', name='betaX_Australia_dim_1'))

    • noise_chol_Canada_corr_dim_0
      PandasIndex

      PandasIndex(Int64Index([0, 1, 2], dtype='int64', name='noise_chol_Canada_corr_dim_0'))

    • noise_chol_Canada_corr_dim_1
      PandasIndex

      PandasIndex(Int64Index([0, 1, 2], dtype='int64', name='noise_chol_Canada_corr_dim_1'))

    • noise_chol_Chile_stds_dim_0
      PandasIndex

      PandasIndex(Int64Index([0, 1, 2], dtype='int64', name='noise_chol_Chile_stds_dim_0'))

    • noise_chol_United Kingdom_dim_0
      PandasIndex

      PandasIndex(Int64Index([0, 1, 2, 3, 4, 5], dtype='int64', name='noise_chol_United Kingdom_dim_0'))

    • noise_chol_Australia_dim_0
      PandasIndex

      PandasIndex(Int64Index([0, 1, 2, 3, 4, 5], dtype='int64', name='noise_chol_Australia_dim_0'))

    • betaX_New Zealand_dim_0
      PandasIndex

      PandasIndex(Int64Index([ 0,  1,  2,  3,  4,  5,  6,  7,  8,  9, 10, 11, 12, 13, 14, 15, 16,
                  17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33,
                  34, 35, 36, 37, 38, 39, 40],
                 dtype='int64', name='betaX_New Zealand_dim_0'))

    • betaX_New Zealand_dim_1
      PandasIndex

      PandasIndex(Int64Index([0, 1, 2], dtype='int64', name='betaX_New Zealand_dim_1'))

    • noise_chol_Australia_corr_dim_0
      PandasIndex

      PandasIndex(Int64Index([0, 1, 2], dtype='int64', name='noise_chol_Australia_corr_dim_0'))

    • noise_chol_Australia_corr_dim_1
      PandasIndex

      PandasIndex(Int64Index([0, 1, 2], dtype='int64', name='noise_chol_Australia_corr_dim_1'))

    • omega_Canada_dim_0
      PandasIndex

      PandasIndex(Int64Index([0, 1, 2], dtype='int64', name='omega_Canada_dim_0'))

    • omega_Canada_dim_1
      PandasIndex

      PandasIndex(Int64Index([0, 1, 2], dtype='int64', name='omega_Canada_dim_1'))

    • noise_chol_Australia_stds_dim_0
      PandasIndex

      PandasIndex(Int64Index([0, 1, 2], dtype='int64', name='noise_chol_Australia_stds_dim_0'))

    • noise_chol_South Africa_corr_dim_0
      PandasIndex

      PandasIndex(Int64Index([0, 1, 2], dtype='int64', name='noise_chol_South Africa_corr_dim_0'))

    • noise_chol_South Africa_corr_dim_1
      PandasIndex

      PandasIndex(Int64Index([0, 1, 2], dtype='int64', name='noise_chol_South Africa_corr_dim_1'))

    • noise_chol_Ireland_dim_0
      PandasIndex

      PandasIndex(Int64Index([0, 1, 2, 3, 4, 5], dtype='int64', name='noise_chol_Ireland_dim_0'))

    • noise_chol_Ireland_corr_dim_0
      PandasIndex

      PandasIndex(Int64Index([0, 1, 2], dtype='int64', name='noise_chol_Ireland_corr_dim_0'))

    • noise_chol_Ireland_corr_dim_1
      PandasIndex

      PandasIndex(Int64Index([0, 1, 2], dtype='int64', name='noise_chol_Ireland_corr_dim_1'))

    • betaX_Chile_dim_0
      PandasIndex

      PandasIndex(Int64Index([ 0,  1,  2,  3,  4,  5,  6,  7,  8,  9, 10, 11, 12, 13, 14, 15, 16,
                  17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33,
                  34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48],
                 dtype='int64', name='betaX_Chile_dim_0'))

    • betaX_Chile_dim_1
      PandasIndex

      PandasIndex(Int64Index([0, 1, 2], dtype='int64', name='betaX_Chile_dim_1'))

    • omega_global_stds_dim_0
      PandasIndex

      PandasIndex(Int64Index([0, 1, 2], dtype='int64', name='omega_global_stds_dim_0'))

    • betaX_South Africa_dim_0
      PandasIndex

      PandasIndex(Int64Index([ 0,  1,  2,  3,  4,  5,  6,  7,  8,  9, 10, 11, 12, 13, 14, 15, 16,
                  17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33,
                  34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48],
                 dtype='int64', name='betaX_South Africa_dim_0'))

    • betaX_South Africa_dim_1
      PandasIndex

      PandasIndex(Int64Index([0, 1, 2], dtype='int64', name='betaX_South Africa_dim_1'))

    • noise_chol_Canada_stds_dim_0
      PandasIndex

      PandasIndex(Int64Index([0, 1, 2], dtype='int64', name='noise_chol_Canada_stds_dim_0'))

    • noise_chol_New Zealand_corr_dim_0
      PandasIndex

      PandasIndex(Int64Index([0, 1, 2], dtype='int64', name='noise_chol_New Zealand_corr_dim_0'))

    • noise_chol_New Zealand_corr_dim_1
      PandasIndex

      PandasIndex(Int64Index([0, 1, 2], dtype='int64', name='noise_chol_New Zealand_corr_dim_1'))

    • noise_chol_United States_corr_dim_0
      PandasIndex

      PandasIndex(Int64Index([0, 1, 2], dtype='int64', name='noise_chol_United States_corr_dim_0'))

    • noise_chol_United States_corr_dim_1
      PandasIndex

      PandasIndex(Int64Index([0, 1, 2], dtype='int64', name='noise_chol_United States_corr_dim_1'))

    • noise_chol_Chile_dim_0
      PandasIndex

      PandasIndex(Int64Index([0, 1, 2, 3, 4, 5], dtype='int64', name='noise_chol_Chile_dim_0'))

    • noise_chol_Ireland_stds_dim_0
      PandasIndex

      PandasIndex(Int64Index([0, 1, 2], dtype='int64', name='noise_chol_Ireland_stds_dim_0'))

  • Attributes: (4)

    created_at :

    2023-02-21T19:22:35.383920

    arviz_version :

    0.14.0

    inference_library :

    pymc

    inference_library_version :

    5.0.1

  
  
• prior_predictive

  <xarray.Dataset>
  Dimensions:                   (chain: 1, draw: 500, obs_Ireland_dim_0: 49,
                                 obs_Ireland_dim_1: 3,
                                 obs_South Africa_dim_0: 49,
                                 obs_South Africa_dim_1: 3,
                                 obs_United States_dim_0: 46,
                                 obs_United States_dim_1: 3, obs_Chile_dim_0: 49,
                                 obs_Chile_dim_1: 3, obs_Canada_dim_0: 22,
                                 obs_Canada_dim_1: 3, obs_New Zealand_dim_0: 41,
                                 obs_New Zealand_dim_1: 3,
                                 obs_United Kingdom_dim_0: 49,
                                 obs_United Kingdom_dim_1: 3,
                                 obs_Australia_dim_0: 49, obs_Australia_dim_1: 3)
  Coordinates: (12/18)
    * chain                     (chain) int64 0
    * draw                      (draw) int64 0 1 2 3 4 5 ... 495 496 497 498 499
    * obs_Ireland_dim_0         (obs_Ireland_dim_0) int64 0 1 2 3 ... 45 46 47 48
    * obs_Ireland_dim_1         (obs_Ireland_dim_1) int64 0 1 2
    * obs_South Africa_dim_0    (obs_South Africa_dim_0) int64 0 1 2 ... 46 47 48
    * obs_South Africa_dim_1    (obs_South Africa_dim_1) int64 0 1 2
      ...                        ...
    * obs_New Zealand_dim_0     (obs_New Zealand_dim_0) int64 0 1 2 3 ... 38 39 40
    * obs_New Zealand_dim_1     (obs_New Zealand_dim_1) int64 0 1 2
    * obs_United Kingdom_dim_0  (obs_United Kingdom_dim_0) int64 0 1 2 ... 47 48
    * obs_United Kingdom_dim_1  (obs_United Kingdom_dim_1) int64 0 1 2
    * obs_Australia_dim_0       (obs_Australia_dim_0) int64 0 1 2 3 ... 46 47 48
    * obs_Australia_dim_1       (obs_Australia_dim_1) int64 0 1 2
  Data variables:
      obs_Ireland               (chain, draw, obs_Ireland_dim_0, obs_Ireland_dim_1) float64 ...
      obs_South Africa          (chain, draw, obs_South Africa_dim_0, obs_South Africa_dim_1) float64 ...
      obs_United States         (chain, draw, obs_United States_dim_0, obs_United States_dim_1) float64 ...
      obs_Chile                 (chain, draw, obs_Chile_dim_0, obs_Chile_dim_1) float64 ...
      obs_Canada                (chain, draw, obs_Canada_dim_0, obs_Canada_dim_1) float64 ...
      obs_New Zealand           (chain, draw, obs_New Zealand_dim_0, obs_New Zealand_dim_1) float64 ...
      obs_United Kingdom        (chain, draw, obs_United Kingdom_dim_0, obs_United Kingdom_dim_1) float64 ...
      obs_Australia             (chain, draw, obs_Australia_dim_0, obs_Australia_dim_1) float64 ...
  Attributes:
      created_at:                 2023-02-21T19:22:35.399482
      arviz_version:              0.14.0
      inference_library:          pymc
      inference_library_version:  5.0.1

  xarray.Dataset

  • Dimensions:
    • chain: 1
    • draw: 500
    • obs_Ireland_dim_0: 49
    • obs_Ireland_dim_1: 3
    • obs_South Africa_dim_0: 49
    • obs_South Africa_dim_1: 3
    • obs_United States_dim_0: 46
    • obs_United States_dim_1: 3
    • obs_Chile_dim_0: 49
    • obs_Chile_dim_1: 3
    • obs_Canada_dim_0: 22
    • obs_Canada_dim_1: 3
    • obs_New Zealand_dim_0: 41
    • obs_New Zealand_dim_1: 3
    • obs_United Kingdom_dim_0: 49
    • obs_United Kingdom_dim_1: 3
    • obs_Australia_dim_0: 49
    • obs_Australia_dim_1: 3
  • Coordinates: (18)
    • chain
      (chain)
      int64
      0

      array([0])

    • draw
      (draw)
      int64
      0 1 2 3 4 5 ... 495 496 497 498 499

      array([  0,   1,   2, ..., 497, 498, 499])

    • obs_Ireland_dim_0
      (obs_Ireland_dim_0)
      int64
      0 1 2 3 4 5 6 ... 43 44 45 46 47 48

      array([ 0,  1,  2,  3,  4,  5,  6,  7,  8,  9, 10, 11, 12, 13, 14, 15, 16, 17,
             18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35,
             36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48])

    • obs_Ireland_dim_1
      (obs_Ireland_dim_1)
      int64
      0 1 2

      array([0, 1, 2])

    • obs_South Africa_dim_0
      (obs_South Africa_dim_0)
      int64
      0 1 2 3 4 5 6 ... 43 44 45 46 47 48

      array([ 0,  1,  2,  3,  4,  5,  6,  7,  8,  9, 10, 11, 12, 13, 14, 15, 16, 17,
             18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35,
             36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48])

    • obs_South Africa_dim_1
      (obs_South Africa_dim_1)
      int64
      0 1 2

      array([0, 1, 2])

    • obs_United States_dim_0
      (obs_United States_dim_0)
      int64
      0 1 2 3 4 5 6 ... 40 41 42 43 44 45

      array([ 0,  1,  2,  3,  4,  5,  6,  7,  8,  9, 10, 11, 12, 13, 14, 15, 16, 17,
             18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35,
             36, 37, 38, 39, 40, 41, 42, 43, 44, 45])

    • obs_United States_dim_1
      (obs_United States_dim_1)
      int64
      0 1 2

      array([0, 1, 2])

    • obs_Chile_dim_0
      (obs_Chile_dim_0)
      int64
      0 1 2 3 4 5 6 ... 43 44 45 46 47 48

      array([ 0,  1,  2,  3,  4,  5,  6,  7,  8,  9, 10, 11, 12, 13, 14, 15, 16, 17,
             18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35,
             36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48])

    • obs_Chile_dim_1
      (obs_Chile_dim_1)
      int64
      0 1 2

      array([0, 1, 2])

    • obs_Canada_dim_0
      (obs_Canada_dim_0)
      int64
      0 1 2 3 4 5 6 ... 16 17 18 19 20 21

      array([ 0,  1,  2,  3,  4,  5,  6,  7,  8,  9, 10, 11, 12, 13, 14, 15, 16, 17,
             18, 19, 20, 21])

    • obs_Canada_dim_1
      (obs_Canada_dim_1)
      int64
      0 1 2

      array([0, 1, 2])

    • obs_New Zealand_dim_0
      (obs_New Zealand_dim_0)
      int64
      0 1 2 3 4 5 6 ... 35 36 37 38 39 40

      array([ 0,  1,  2,  3,  4,  5,  6,  7,  8,  9, 10, 11, 12, 13, 14, 15, 16, 17,
             18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35,
             36, 37, 38, 39, 40])

    • obs_New Zealand_dim_1
      (obs_New Zealand_dim_1)
      int64
      0 1 2

      array([0, 1, 2])

    • obs_United Kingdom_dim_0
      (obs_United Kingdom_dim_0)
      int64
      0 1 2 3 4 5 6 ... 43 44 45 46 47 48

      array([ 0,  1,  2,  3,  4,  5,  6,  7,  8,  9, 10, 11, 12, 13, 14, 15, 16, 17,
             18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35,
             36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48])

    • obs_United Kingdom_dim_1
      (obs_United Kingdom_dim_1)
      int64
      0 1 2

      array([0, 1, 2])

    • obs_Australia_dim_0
      (obs_Australia_dim_0)
      int64
      0 1 2 3 4 5 6 ... 43 44 45 46 47 48

      array([ 0,  1,  2,  3,  4,  5,  6,  7,  8,  9, 10, 11, 12, 13, 14, 15, 16, 17,
             18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35,
             36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48])

    • obs_Australia_dim_1
      (obs_Australia_dim_1)
      int64
      0 1 2

      array([0, 1, 2])

  • Data variables: (8)
    • obs_Ireland
      (chain, draw, obs_Ireland_dim_0, obs_Ireland_dim_1)
      float64
      1.442 1.214 ... -1.998 -0.2268

      array([[[[ 1.44216392,  1.21433603, -0.24620373],
               [-0.29216679, -2.39120885, -0.22496641],
               [-1.20296202, -2.54566872, -0.22978156],
               ...,
               [ 5.4151822 , -0.20693587,  0.24666736],
               [ 1.72677909,  0.93029297, -0.45735838],
               [-1.82894206, -2.75633625, -0.14823089]],
      
              [[ 1.86050196,  0.3829668 , -1.76367683],
               [ 1.34522644,  0.89586816, -1.46318557],
               [-1.83455167, -1.14518294,  1.74751655],
               ...,
               [ 0.67964042, -2.60436758,  0.47356766],
               [-0.30570083,  1.05962613, -0.32873821],
               [-0.41864025, -0.98748916,  0.65666947]],
      
              [[ 0.09244337, -0.96028434, -0.05410173],
               [ 0.3888446 , -1.45914636,  0.65642348],
               [ 0.35328146,  0.57956438,  0.48289132],
               ...,
      ...
               ...,
               [-0.65047194,  0.20260695,  0.48688026],
               [ 1.06195943,  0.93297824,  0.58146274],
               [-1.04956009,  0.17975547, -0.87755078]],
      
              [[-0.05558822,  0.64847547,  0.87191278],
               [ 1.53149986, -0.87046858,  1.462854  ],
               [-0.78521177,  0.36727654,  0.30958242],
               ...,
               [ 1.36300562,  0.33760491,  0.85538822],
               [ 2.0075936 , -0.53134895, -0.10552448],
               [ 1.06922899, -0.772015  , -0.22834952]],
      
              [[ 1.22562894,  1.1954118 , -1.77726454],
               [ 1.32047634,  0.26520605, -0.18302668],
               [ 2.92656349,  3.24812927,  0.34441356],
               ...,
               [ 2.83626309,  2.9921436 , -0.40669417],
               [-0.61613114, -0.41848802, -1.38183079],
               [-2.20019105, -1.99845853, -0.22684925]]]])

    • obs_South Africa
      (chain, draw, obs_South Africa_dim_0, obs_South Africa_dim_1)
      float64
      -1.08 -1.475 ... -3.026 -0.4278

      array([[[[-1.08042815, -1.47486374, -0.18998885],
               [-2.22090256, -0.52845789,  0.14413059],
               [ 0.18061971,  0.13006436, -0.25252454],
               ...,
               [ 0.83959636, -0.62210856, -0.34175715],
               [-0.18503247,  1.01256311,  0.01452391],
               [-0.94098186,  0.48988045, -0.19091588]],
      
              [[-0.96874486,  0.67375781,  1.19963497],
               [-1.68355957,  0.8223419 ,  0.86117177],
               [ 3.29639347, -1.39216596, -2.36671704],
               ...,
               [-1.1907885 , -1.08244153,  0.53956029],
               [ 1.02026952, -0.45850167,  0.26503035],
               [-0.57281338,  0.41690366, -0.31898268]],
      
              [[ 0.90392978,  0.12189939, -0.89010113],
               [ 0.23838208, -0.07178184,  0.31858745],
               [ 0.65777894,  0.94456795,  0.6605204 ],
               ...,
      ...
               ...,
               [ 1.20299772,  0.63924542,  0.76281646],
               [ 1.14701949,  0.01895048, -1.16792918],
               [ 1.07097969, -0.10581595, -0.92965169]],
      
              [[ 0.404994  ,  0.17072219, -0.25864754],
               [ 0.91183848,  1.87827984,  0.2626324 ],
               [-0.62801688, -0.96702257, -0.17971642],
               ...,
               [-0.61541632, -0.38355841, -0.73965677],
               [-0.37693426,  1.51279364,  0.51928169],
               [-0.76537358, -0.98890974,  0.02919827]],
      
              [[ 1.06355078,  1.35670492, -0.43499497],
               [-0.49787069, -0.89534819, -0.59284817],
               [-0.39022683, -0.01694431, -1.06289771],
               ...,
               [-0.3023473 , -0.23479384, -0.74991632],
               [ 2.45133219,  3.44020825, -0.8500616 ],
               [-2.67742504, -3.0255616 , -0.42784937]]]])

    • obs_United States
      (chain, draw, obs_United States_dim_0, obs_United States_dim_1)
      float64
      2.089 -2.226 ... -2.025 -0.3652

      array([[[[ 2.08853197, -2.22588785, -0.58962537],
               [-0.10969838,  1.34801774, -0.52620355],
               [-0.90904737,  0.38794311, -0.01206754],
               ...,
               [ 1.24994634,  0.70346244,  0.28820293],
               [ 0.18712305, -2.0775857 , -0.26144148],
               [ 0.36701772,  0.42406919, -0.20399696]],
      
              [[ 0.43927676,  0.05106411, -0.39859406],
               [-0.12982463,  1.12329005,  0.0893416 ],
               [ 0.0298152 ,  1.28654773, -0.27773953],
               ...,
               [-0.71448065, -0.1567184 ,  0.606019  ],
               [-0.99729536,  3.2019223 , -0.25898444],
               [ 0.05618898, -0.29531048,  0.24716793]],
      
              [[ 0.1088473 ,  0.46556288,  2.20590056],
               [-1.93142753,  0.38205921,  2.50283913],
               [-0.48950337, -1.06061476, -0.06973738],
               ...,
      ...
               ...,
               [ 0.50105365, -0.16590621, -4.01649351],
               [ 0.24845363,  0.05301149,  1.30080469],
               [-0.35403633,  0.26474948,  0.19587305]],
      
              [[ 0.36636661, -0.48933288,  0.5562534 ],
               [ 0.83096629,  0.4422902 ,  0.53408087],
               [ 1.32701595, -2.33520178,  0.33690979],
               ...,
               [-0.01116044,  0.19162144,  0.43105356],
               [ 1.07767062, -1.90503447, -0.1494513 ],
               [ 2.16704744, -1.31648337, -0.04139058]],
      
              [[-0.56202632, -0.43752455, -0.27313303],
               [-2.48768493, -3.07775194, -0.65138619],
               [-0.81996858, -0.76701832,  0.25229919],
               ...,
               [-0.05610424,  0.1457594 , -1.22410613],
               [-4.3172488 , -4.36695607, -1.04569734],
               [-2.24153764, -2.02481296, -0.36521949]]]])

    • obs_Chile
      (chain, draw, obs_Chile_dim_0, obs_Chile_dim_1)
      float64
      -0.2398 -0.555 ... -0.5953 -0.1403

      array([[[[-0.23983271, -0.55496307, -0.32546261],
               [ 2.65740345,  0.27049439,  1.4947758 ],
               [-0.46034862,  0.47972309, -0.18367752],
               ...,
               [-0.95509841, -0.14319467, -0.2346776 ],
               [-0.7353475 , -0.56112571, -0.17695423],
               [ 0.69757888, -0.2706058 , -0.09177315]],
      
              [[ 1.50715309,  0.45717434, -1.48379218],
               [-0.7717147 ,  2.7121891 ,  0.07460517],
               [ 0.7450025 ,  0.69279186, -0.68221752],
               ...,
               [-1.88908705,  1.36096753,  0.98561717],
               [-0.05317145,  1.00672431, -0.2189253 ],
               [ 1.88091604, -0.35806087, -1.30143482]],
      
              [[ 5.38281052, -0.60435078,  3.84112732],
               [ 1.38303577,  0.41621645,  1.08785577],
               [ 0.64042152, -0.11685234, -1.46692512],
               ...,
      ...
               ...,
               [-0.01658554,  1.45378278, -0.12856442],
               [ 0.20198539,  2.90396268,  0.25314398],
               [-0.22151684, -1.1588733 ,  0.40549707]],
      
              [[ 0.94490597,  1.7444274 ,  0.92247364],
               [ 0.26286682, -0.84164471,  0.52252032],
               [-0.47989137,  2.09021485,  1.27009669],
               ...,
               [ 0.7860727 ,  0.30765822, -1.3157127 ],
               [-0.46221212,  1.88805901, -0.97950823],
               [-0.32482327,  0.27650055,  1.32142354]],
      
              [[-1.90786146, -2.28417557, -0.5581007 ],
               [-0.64835244, -1.90706006,  0.14107129],
               [ 2.35462028,  1.47455725,  0.37631502],
               ...,
               [-0.16268285,  1.58034517, -1.64781457],
               [-1.79508319, -2.65565003,  0.42062359],
               [-1.14180525, -0.59525268, -0.14033109]]]])

    • obs_Canada
      (chain, draw, obs_Canada_dim_0, obs_Canada_dim_1)
      float64
      2.987 -1.596 ... 0.9749 0.4238

      array([[[[ 2.98660411, -1.59648976,  0.02776848],
               [ 2.30760763, -0.90014747, -1.37311418],
               [-1.34691522, -0.51156209, -0.91005974],
               ...,
               [-0.26104631,  0.4777054 , -0.13301976],
               [ 1.97676618, -0.15473958,  1.36435682],
               [ 1.33046223, -0.17425685,  0.6712027 ]],
      
              [[-0.80795108, -0.64994571,  0.99029705],
               [ 0.53232811,  0.07427657, -0.42027595],
               [-0.67383398,  0.72604355,  0.50428044],
               ...,
               [-0.56489111,  2.43644893, -0.04659438],
               [ 0.22243535, -2.58961294,  0.81879761],
               [-1.17388754,  0.70958432,  1.00067421]],
      
              [[ 0.32959532, -0.56568257, -0.41270325],
               [ 0.33805488,  1.55197966,  0.38555987],
               [ 0.40486586, -1.44468415,  1.79171157],
               ...,
      ...
               ...,
               [ 0.45944104, -0.12098934, -1.62095287],
               [-0.30234169,  0.91677438, -0.77668383],
               [ 0.40048151,  1.21934097,  0.1267496 ]],
      
              [[ 0.47931881, -0.64326409,  2.6489885 ],
               [ 0.67076413, -0.62735388,  0.33671592],
               [ 4.16374303, -0.48509279,  1.87181408],
               ...,
               [ 1.92751611, -1.02713286,  0.51161177],
               [ 2.24039588,  2.5608276 ,  3.3617624 ],
               [ 4.46036862, -1.56867684,  1.78854956]],
      
              [[-0.74379176, -0.13221482, -0.97135126],
               [-1.12372226, -1.04658563, -1.19400086],
               [ 1.68300538,  1.53496957, -0.64640167],
               ...,
               [-2.2878875 , -1.25458378, -1.04748576],
               [ 2.32948378,  1.53639997, -1.66119426],
               [ 1.2399767 ,  0.97493392,  0.42379137]]]])

    • obs_New Zealand
      (chain, draw, obs_New Zealand_dim_0, obs_New Zealand_dim_1)
      float64
      1.055 -0.1359 ... -1.389 0.5238

      array([[[[ 1.05523252, -0.13593232,  0.34285394],
               [ 1.10724659, -0.22494669,  0.38763203],
               [ 1.10306878,  0.13183832,  0.28809004],
               ...,
               [ 0.63228329, -0.14917731, -0.86728425],
               [ 1.48214696, -0.106533  , -0.01250324],
               [-0.19633409,  0.06782761, -0.72674219]],
      
              [[-1.45176185,  0.86840139,  0.85946383],
               [-0.93452266,  0.80516561,  0.48220917],
               [-2.45383128,  2.5491863 ,  1.10627156],
               ...,
               [ 0.11443249, -1.17622893,  0.36837752],
               [-3.3279085 ,  1.93894   ,  2.30954749],
               [-1.6718716 ,  0.49667556,  1.25951951]],
      
              [[ 0.04847526, -2.17173998, -0.59243999],
               [ 1.02471664, -1.73180326,  1.5968373 ],
               [-0.34959728,  1.94235375, -1.03645308],
               ...,
      ...
               ...,
               [ 0.31642202,  0.53061372,  0.75828846],
               [-0.01783574, -0.1485634 , -0.3748505 ],
               [ 0.26475625,  0.49328303, -0.63879072]],
      
              [[ 0.41255484,  0.33032059, -0.60283073],
               [-1.94941087, -0.87270202, -1.20654958],
               [-2.46339777,  0.22859426, -1.38589276],
               ...,
               [ 0.63739327,  0.26510252,  1.22511094],
               [-1.152238  ,  0.57430785,  1.73773102],
               [ 1.85377782, -0.57949193,  1.67061952]],
      
              [[ 0.56362365,  0.29930631, -1.52660782],
               [-2.37537378, -3.19383251,  2.00526821],
               [-0.10600629,  0.73408653, -0.23659082],
               ...,
               [ 2.07984589,  2.2624388 ,  0.99146509],
               [-1.87705982, -2.67770578, -1.0458133 ],
               [-1.31605037, -1.38868301,  0.52380847]]]])

    • obs_United Kingdom
      (chain, draw, obs_United Kingdom_dim_0, obs_United Kingdom_dim_1)
      float64
      1.107 -2.117 ... -0.7776 -0.8262

      array([[[[ 1.10738845, -2.11722522, -0.35746766],
               [ 1.55223399,  2.62762349, -0.16935803],
               [-0.44632279, -2.35956383, -0.01947456],
               ...,
               [ 0.18994703,  1.66294906, -0.25094526],
               [ 0.3716922 , -0.3117239 , -0.02782261],
               [ 0.7887149 , -0.66596306, -0.2303511 ]],
      
              [[-0.71891412, -1.46268714,  1.23698941],
               [-0.93229571,  1.22427462,  0.0601163 ],
               [ 0.56910366,  0.48965776, -0.67313399],
               ...,
               [-1.29604265,  2.8609556 ,  1.05316722],
               [ 0.03062841,  1.7680467 , -0.27597323],
               [ 1.88690148, -1.52340342, -0.49127921]],
      
              [[ 0.31584015, -0.12397509,  0.75474332],
               [-0.24685663,  0.13060596,  0.3601289 ],
               [ 0.13992027, -0.03836627,  0.45646398],
               ...,
      ...
               ...,
               [ 0.57405796,  0.09665485,  0.03985287],
               [-2.51254281,  0.67780332,  0.27077475],
               [ 1.33433029, -0.04570146,  0.17439368]],
      
              [[ 0.09309161,  0.55771717,  0.57979781],
               [ 3.18335899, -0.35302318, -0.73893789],
               [-1.1142341 ,  0.17748681,  0.63689114],
               ...,
               [-0.45750183,  0.28319619,  0.53701605],
               [ 0.26386199,  0.26702223, -0.1595756 ],
               [ 0.52050313,  0.33525292, -0.75879134]],
      
              [[-3.57813703, -2.23288716, -2.70898962],
               [ 2.17291994,  1.40198545,  0.85217644],
               [-3.28761705, -2.31308783,  0.59479336],
               ...,
               [ 0.35926463, -0.04177487, -2.39238352],
               [ 2.68620149,  2.01590833, -0.99310651],
               [-2.05764241, -0.7776359 , -0.82616616]]]])

    • obs_Australia
      (chain, draw, obs_Australia_dim_0, obs_Australia_dim_1)
      float64
      -5.604 -0.2084 ... -0.9151 -0.07599

      array([[[[-5.60393572e+00, -2.08367889e-01, -5.34531446e-01],
               [-1.50689758e+00, -5.77504918e-01, -6.70400497e-01],
               [ 1.59242235e+00,  1.12682024e-02,  1.84156820e-01],
               ...,
               [ 1.14049351e+00, -2.20449941e-01, -3.63655669e-01],
               [ 7.36214659e-01,  1.17890333e-01,  3.28919007e-01],
               [-1.61922809e+00,  3.29915836e-01,  1.44851794e-01]],
      
              [[ 2.63927117e+00, -1.53513527e+00, -1.09620961e-01],
               [ 3.58209032e-01,  4.64295322e-02,  2.47855405e-01],
               [-2.20697192e+00,  1.55617999e-01,  9.23830722e-01],
               ...,
               [-9.26518306e-01,  2.72831592e+00, -9.81586410e-01],
               [ 1.48436501e+00,  8.39778239e-01, -1.10045548e+00],
               [-1.75706361e-01,  1.67216355e+00, -8.29995090e-02]],
      
              [[ 3.90776771e-01,  8.08349220e-01,  9.65900633e-02],
               [ 3.36658728e-01,  3.14831015e-01, -1.62908539e-01],
               [ 2.36358106e-01,  1.33925410e+00, -8.62401016e-02],
               ...,
      ...
               ...,
               [-3.48177967e-01,  7.69201252e-02, -4.36393500e-01],
               [ 2.40615919e-01, -1.39237716e-01,  2.23500298e-01],
               [ 4.94323748e-01,  4.57505097e-02, -3.20458296e-06]],
      
              [[-2.48806518e+00,  9.12924257e-01,  1.32764793e-01],
               [-1.64769461e+00,  6.10682508e-02, -1.13931263e+00],
               [-1.16813627e+00,  8.23503325e-02, -2.64580168e+00],
               ...,
               [ 5.11267528e-01,  2.39102062e-01,  6.47469253e-01],
               [ 2.90856041e+00, -2.22564814e-01,  1.33412563e+00],
               [-3.85778035e-01,  2.87312627e-01, -3.41999226e-01]],
      
              [[ 9.37939769e-01,  1.02722270e+00,  1.58903612e-01],
               [ 1.92159493e-01, -1.33098265e-01, -4.73658285e-01],
               [-3.85149807e+00, -2.39606350e+00, -7.20505580e-01],
               ...,
               [-2.54402056e-01, -4.37774476e-01,  8.59884653e-01],
               [-1.53794252e+00, -9.67771004e-01,  4.47421046e-01],
               [ 3.87364370e-01, -9.15064981e-01, -7.59942798e-02]]]])

  • Indexes: (18)
    • chain
      PandasIndex

      PandasIndex(Int64Index([0], dtype='int64', name='chain'))

    • draw
      PandasIndex

      PandasIndex(Int64Index([  0,   1,   2,   3,   4,   5,   6,   7,   8,   9,
                  ...
                  490, 491, 492, 493, 494, 495, 496, 497, 498, 499],
                 dtype='int64', name='draw', length=500))

    • obs_Ireland_dim_0
      PandasIndex

      PandasIndex(Int64Index([ 0,  1,  2,  3,  4,  5,  6,  7,  8,  9, 10, 11, 12, 13, 14, 15, 16,
                  17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33,
                  34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48],
                 dtype='int64', name='obs_Ireland_dim_0'))

    • obs_Ireland_dim_1
      PandasIndex

      PandasIndex(Int64Index([0, 1, 2], dtype='int64', name='obs_Ireland_dim_1'))

    • obs_South Africa_dim_0
      PandasIndex

      PandasIndex(Int64Index([ 0,  1,  2,  3,  4,  5,  6,  7,  8,  9, 10, 11, 12, 13, 14, 15, 16,
                  17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33,
                  34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48],
                 dtype='int64', name='obs_South Africa_dim_0'))

    • obs_South Africa_dim_1
      PandasIndex

      PandasIndex(Int64Index([0, 1, 2], dtype='int64', name='obs_South Africa_dim_1'))

    • obs_United States_dim_0
      PandasIndex

      PandasIndex(Int64Index([ 0,  1,  2,  3,  4,  5,  6,  7,  8,  9, 10, 11, 12, 13, 14, 15, 16,
                  17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33,
                  34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45],
                 dtype='int64', name='obs_United States_dim_0'))

    • obs_United States_dim_1
      PandasIndex

      PandasIndex(Int64Index([0, 1, 2], dtype='int64', name='obs_United States_dim_1'))

    • obs_Chile_dim_0
      PandasIndex

      PandasIndex(Int64Index([ 0,  1,  2,  3,  4,  5,  6,  7,  8,  9, 10, 11, 12, 13, 14, 15, 16,
                  17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33,
                  34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48],
                 dtype='int64', name='obs_Chile_dim_0'))

    • obs_Chile_dim_1
      PandasIndex

      PandasIndex(Int64Index([0, 1, 2], dtype='int64', name='obs_Chile_dim_1'))

    • obs_Canada_dim_0
      PandasIndex

      PandasIndex(Int64Index([0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18,
                  19, 20, 21],
                 dtype='int64', name='obs_Canada_dim_0'))

    • obs_Canada_dim_1
      PandasIndex

      PandasIndex(Int64Index([0, 1, 2], dtype='int64', name='obs_Canada_dim_1'))

    • obs_New Zealand_dim_0
      PandasIndex

      PandasIndex(Int64Index([ 0,  1,  2,  3,  4,  5,  6,  7,  8,  9, 10, 11, 12, 13, 14, 15, 16,
                  17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33,
                  34, 35, 36, 37, 38, 39, 40],
                 dtype='int64', name='obs_New Zealand_dim_0'))

    • obs_New Zealand_dim_1
      PandasIndex

      PandasIndex(Int64Index([0, 1, 2], dtype='int64', name='obs_New Zealand_dim_1'))

    • obs_United Kingdom_dim_0
      PandasIndex

      PandasIndex(Int64Index([ 0,  1,  2,  3,  4,  5,  6,  7,  8,  9, 10, 11, 12, 13, 14, 15, 16,
                  17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33,
                  34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48],
                 dtype='int64', name='obs_United Kingdom_dim_0'))

    • obs_United Kingdom_dim_1
      PandasIndex

      PandasIndex(Int64Index([0, 1, 2], dtype='int64', name='obs_United Kingdom_dim_1'))

    • obs_Australia_dim_0
      PandasIndex

      PandasIndex(Int64Index([ 0,  1,  2,  3,  4,  5,  6,  7,  8,  9, 10, 11, 12, 13, 14, 15, 16,
                  17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33,
                  34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48],
                 dtype='int64', name='obs_Australia_dim_0'))

    • obs_Australia_dim_1
      PandasIndex

      PandasIndex(Int64Index([0, 1, 2], dtype='int64', name='obs_Australia_dim_1'))

  • Attributes: (4)

    created_at :

    2023-02-21T19:22:35.399482

    arviz_version :

    0.14.0

    inference_library :

    pymc

    inference_library_version :

    5.0.1

  
  
• observed_data

  <xarray.Dataset>
  Dimensions:                   (obs_Australia_dim_0: 49, obs_Australia_dim_1: 3,
                                 obs_Canada_dim_0: 22, obs_Canada_dim_1: 3,
                                 obs_Chile_dim_0: 49, obs_Chile_dim_1: 3,
                                 obs_Ireland_dim_0: 49, obs_Ireland_dim_1: 3,
                                 obs_New Zealand_dim_0: 41,
                                 obs_New Zealand_dim_1: 3,
                                 obs_South Africa_dim_0: 49,
                                 obs_South Africa_dim_1: 3,
                                 obs_United Kingdom_dim_0: 49,
                                 obs_United Kingdom_dim_1: 3,
                                 obs_United States_dim_0: 46,
                                 obs_United States_dim_1: 3)
  Coordinates: (12/16)
    * obs_Australia_dim_0       (obs_Australia_dim_0) int64 0 1 2 3 ... 46 47 48
    * obs_Australia_dim_1       (obs_Australia_dim_1) int64 0 1 2
    * obs_Canada_dim_0          (obs_Canada_dim_0) int64 0 1 2 3 4 ... 18 19 20 21
    * obs_Canada_dim_1          (obs_Canada_dim_1) int64 0 1 2
    * obs_Chile_dim_0           (obs_Chile_dim_0) int64 0 1 2 3 4 ... 45 46 47 48
    * obs_Chile_dim_1           (obs_Chile_dim_1) int64 0 1 2
      ...                        ...
    * obs_South Africa_dim_0    (obs_South Africa_dim_0) int64 0 1 2 ... 46 47 48
    * obs_South Africa_dim_1    (obs_South Africa_dim_1) int64 0 1 2
    * obs_United Kingdom_dim_0  (obs_United Kingdom_dim_0) int64 0 1 2 ... 47 48
    * obs_United Kingdom_dim_1  (obs_United Kingdom_dim_1) int64 0 1 2
    * obs_United States_dim_0   (obs_United States_dim_0) int64 0 1 2 ... 43 44 45
    * obs_United States_dim_1   (obs_United States_dim_1) int64 0 1 2
  Data variables:
      obs_Australia             (obs_Australia_dim_0, obs_Australia_dim_1) float64 ...
      obs_Canada                (obs_Canada_dim_0, obs_Canada_dim_1) float64 0....
      obs_Chile                 (obs_Chile_dim_0, obs_Chile_dim_1) float64 -0.0...
      obs_Ireland               (obs_Ireland_dim_0, obs_Ireland_dim_1) float64 ...
      obs_New Zealand           (obs_New Zealand_dim_0, obs_New Zealand_dim_1) float64 ...
      obs_South Africa          (obs_South Africa_dim_0, obs_South Africa_dim_1) float64 ...
      obs_United Kingdom        (obs_United Kingdom_dim_0, obs_United Kingdom_dim_1) float64 ...
      obs_United States         (obs_United States_dim_0, obs_United States_dim_1) float64 ...
  Attributes:
      created_at:                 2023-02-21T19:22:35.401625
      arviz_version:              0.14.0
      inference_library:          pymc
      inference_library_version:  5.0.1

  xarray.Dataset

  • Dimensions:
    • obs_Australia_dim_0: 49
    • obs_Australia_dim_1: 3
    • obs_Canada_dim_0: 22
    • obs_Canada_dim_1: 3
    • obs_Chile_dim_0: 49
    • obs_Chile_dim_1: 3
    • obs_Ireland_dim_0: 49
    • obs_Ireland_dim_1: 3
    • obs_New Zealand_dim_0: 41
    • obs_New Zealand_dim_1: 3
    • obs_South Africa_dim_0: 49
    • obs_South Africa_dim_1: 3
    • obs_United Kingdom_dim_0: 49
    • obs_United Kingdom_dim_1: 3
    • obs_United States_dim_0: 46
    • obs_United States_dim_1: 3
  • Coordinates: (16)
    • obs_Australia_dim_0
      (obs_Australia_dim_0)
      int64
      0 1 2 3 4 5 6 ... 43 44 45 46 47 48

      array([ 0,  1,  2,  3,  4,  5,  6,  7,  8,  9, 10, 11, 12, 13, 14, 15, 16, 17,
             18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35,
             36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48])

    • obs_Australia_dim_1
      (obs_Australia_dim_1)
      int64
      0 1 2

      array([0, 1, 2])

    • obs_Canada_dim_0
      (obs_Canada_dim_0)
      int64
      0 1 2 3 4 5 6 ... 16 17 18 19 20 21

      array([ 0,  1,  2,  3,  4,  5,  6,  7,  8,  9, 10, 11, 12, 13, 14, 15, 16, 17,
             18, 19, 20, 21])

    • obs_Canada_dim_1
      (obs_Canada_dim_1)
      int64
      0 1 2

      array([0, 1, 2])

    • obs_Chile_dim_0
      (obs_Chile_dim_0)
      int64
      0 1 2 3 4 5 6 ... 43 44 45 46 47 48

      array([ 0,  1,  2,  3,  4,  5,  6,  7,  8,  9, 10, 11, 12, 13, 14, 15, 16, 17,
             18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35,
             36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48])

    • obs_Chile_dim_1
      (obs_Chile_dim_1)
      int64
      0 1 2

      array([0, 1, 2])

    • obs_Ireland_dim_0
      (obs_Ireland_dim_0)
      int64
      0 1 2 3 4 5 6 ... 43 44 45 46 47 48

      array([ 0,  1,  2,  3,  4,  5,  6,  7,  8,  9, 10, 11, 12, 13, 14, 15, 16, 17,
             18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35,
             36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48])

    • obs_Ireland_dim_1
      (obs_Ireland_dim_1)
      int64
      0 1 2

      array([0, 1, 2])

    • obs_New Zealand_dim_0
      (obs_New Zealand_dim_0)
      int64
      0 1 2 3 4 5 6 ... 35 36 37 38 39 40

      array([ 0,  1,  2,  3,  4,  5,  6,  7,  8,  9, 10, 11, 12, 13, 14, 15, 16, 17,
             18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35,
             36, 37, 38, 39, 40])

    • obs_New Zealand_dim_1
      (obs_New Zealand_dim_1)
      int64
      0 1 2

      array([0, 1, 2])

    • obs_South Africa_dim_0
      (obs_South Africa_dim_0)
      int64
      0 1 2 3 4 5 6 ... 43 44 45 46 47 48

      array([ 0,  1,  2,  3,  4,  5,  6,  7,  8,  9, 10, 11, 12, 13, 14, 15, 16, 17,
             18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35,
             36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48])

    • obs_South Africa_dim_1
      (obs_South Africa_dim_1)
      int64
      0 1 2

      array([0, 1, 2])

    • obs_United Kingdom_dim_0
      (obs_United Kingdom_dim_0)
      int64
      0 1 2 3 4 5 6 ... 43 44 45 46 47 48

      array([ 0,  1,  2,  3,  4,  5,  6,  7,  8,  9, 10, 11, 12, 13, 14, 15, 16, 17,
             18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35,
             36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48])

    • obs_United Kingdom_dim_1
      (obs_United Kingdom_dim_1)
      int64
      0 1 2

      array([0, 1, 2])

    • obs_United States_dim_0
      (obs_United States_dim_0)
      int64
      0 1 2 3 4 5 6 ... 40 41 42 43 44 45

      array([ 0,  1,  2,  3,  4,  5,  6,  7,  8,  9, 10, 11, 12, 13, 14, 15, 16, 17,
             18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35,
             36, 37, 38, 39, 40, 41, 42, 43, 44, 45])

    • obs_United States_dim_1
      (obs_United States_dim_1)
      int64
      0 1 2

      array([0, 1, 2])

  • Data variables: (8)
    • obs_Australia
      (obs_Australia_dim_0, obs_Australia_dim_1)
      float64
      0.02585 0.04286 ... 0.02312 0.02713

      array([[ 2.58547961e-02,  4.28564292e-02,  3.01291574e-02],
             [ 4.02342322e-02,  5.34089284e-02,  4.17959536e-02],
             [ 1.32680519e-02,  5.55138348e-02, -6.62524913e-02],
             [ 2.55832078e-02,  2.47380310e-02,  3.37743618e-02],
             [ 3.52982455e-02,  4.08175306e-02,  3.81639772e-02],
             [ 8.90130652e-03,  2.17807603e-02,  3.76296913e-02],
             [ 3.97088688e-02,  1.91113918e-02,  9.32662671e-02],
             [ 2.99024255e-02,  1.88280936e-02,  2.83222198e-02],
             [ 3.28427956e-02,  3.49877208e-02,  1.20346340e-01],
             [ 3.26885389e-02,  4.47891940e-02,  7.00031593e-02],
             [-2.24702705e-02,  2.40914115e-02, -9.94876459e-02],
             [ 4.49343999e-02,  1.93523407e-02,  4.95572988e-02],
             [ 5.11883837e-02,  2.38045459e-02,  9.17559621e-02],
             [ 3.95184383e-02,  4.42945925e-02,  5.76147242e-02],
             [ 2.51601327e-02,  2.32608503e-02,  3.85592131e-03],
             [ 5.58478462e-02,  3.26020154e-02,  7.22331578e-02],
             [ 3.79164057e-02,  4.11176562e-02,  1.01848719e-01],
             [ 3.51113862e-02,  3.83006373e-02,  9.02173419e-03],
             [-3.95869708e-03,  1.50128092e-02, -9.95998900e-02],
             [ 4.12926667e-03,  2.35802217e-02, -4.07912299e-02],
      ...
             [ 3.93603828e-02,  3.05145425e-02,  8.73148213e-02],
             [ 3.06293466e-02,  3.86425685e-02,  1.18382423e-01],
             [ 4.11942154e-02,  4.96800641e-02,  8.37471749e-02],
             [ 3.11142746e-02,  4.10141391e-02,  5.91564733e-02],
             [ 2.69037608e-02,  3.16772386e-02,  7.94902106e-02],
             [ 3.69921502e-02,  4.62949959e-02,  4.42069118e-02],
             [ 3.51452551e-02,  4.28133874e-02,  8.39925571e-02],
             [ 1.84962064e-02,  1.19790989e-02,  1.51249834e-02],
             [ 2.14907809e-02,  2.91778938e-02,  1.73281695e-02],
             [ 2.43974109e-02,  3.82530099e-02,  3.53663916e-02],
             [ 3.84258056e-02,  3.06389144e-02,  1.09774809e-01],
             [ 2.56698119e-02,  1.53975077e-02,  2.85034459e-02],
             [ 2.53063902e-02,  2.03530897e-02, -1.90696114e-02],
             [ 2.14894856e-02,  2.45858631e-02, -3.76203585e-02],
             [ 2.70473314e-02,  3.06920086e-02, -3.71083141e-02],
             [ 2.26996714e-02,  2.99812162e-02, -3.91306699e-04],
             [ 2.83053226e-02,  2.86940855e-02,  4.72726441e-02],
             [ 2.09113206e-02,  2.40001483e-02, -1.28781610e-02],
             [-3.83663216e-05, -4.17408601e-03, -2.50317561e-02],
             [ 1.46438819e-02,  2.31248682e-02,  2.71311126e-02]])

    • obs_Canada
      (obs_Canada_dim_0, obs_Canada_dim_1)
      float64
      0.04801 0.03828 ... 0.04888 0.06909

      array([[ 0.04800665,  0.0382813 ,  0.04941686],
             [ 0.01395742,  0.02626848,  0.04706986],
             [ 0.03364893,  0.03478331,  0.00991683],
             [ 0.03740262,  0.02741445,  0.05085894],
             [ 0.03839372,  0.02711028,  0.08098272],
             [ 0.04875074,  0.03124278,  0.08731537],
             [ 0.04081384,  0.03747819,  0.06090471],
             [ 0.06642994,  0.03802772,  0.03118513],
             [ 0.0100258 ,  0.03149776,  0.0161345 ],
             [-0.02972134,  0.00777432, -0.12006804],
             [ 0.0304273 ,  0.03166653,  0.10895903],
             [ 0.03098382,  0.01992693,  0.04532905],
             [ 0.01746875,  0.01554452,  0.04770492],
             [ 0.02302412,  0.01671947,  0.01438519],
             [ 0.02829622,  0.02010709,  0.02225279],
             [ 0.00657014,  0.02045177, -0.05350516],
             [ 0.00996414,  0.01997434, -0.04765361],
             [ 0.02994591,  0.03212583,  0.03291847],
             [ 0.0273918 ,  0.02606687,  0.01802123],
             [ 0.01862146,  0.01724382,  0.00255267],
             [-0.0537492 , -0.04666877, -0.02469412],
             [ 0.04461856,  0.04887529,  0.06908599]])

    • obs_Chile
      (obs_Chile_dim_0, obs_Chile_dim_1)
      float64
      -0.0516 -0.05632 ... 0.1669 0.162

      array([[-0.05160122, -0.05632364, -0.06215139],
             [ 0.02354219, -0.15455255,  0.17491378],
             [-0.13825224, -0.11897169, -0.25839899],
             [ 0.03760965,  0.0018707 , -0.16035492],
             [ 0.09934463,  0.12915606,  0.14364864],
             [ 0.07418965,  0.07139739,  0.16021225],
             [ 0.08082675,  0.06701527,  0.15572056],
             [ 0.07683715,  0.04286705,  0.19806412],
             [ 0.06321299,  0.10368039,  0.15493248],
             [-0.11669456, -0.14008232, -0.48290291],
             [-0.05147669, -0.05200956, -0.16292912],
             [ 0.04021717,  0.00408348,  0.17264662],
             [ 0.03931606, -0.00438434,  0.09508209],
             [ 0.05238078,  0.04793333,  0.02389143],
             [ 0.06260354,  0.05494253,  0.19649118],
             [ 0.07087879,  0.06314511,  0.13236687],
             [ 0.09461342,  0.08821887,  0.26234943],
             [ 0.03279207,  0.0198484 ,  0.02485722],
             [ 0.07514822,  0.07836482, -0.00177746],
             [ 0.10586076,  0.11977667,  0.21531643],
      ...
             [ 0.03152579,  0.02513677,  0.04334088],
             [ 0.04615093,  0.03353653,  0.08202795],
             [ 0.06460965,  0.07738999,  0.12455842],
             [ 0.05673042,  0.07012815,  0.20768463],
             [ 0.05874041,  0.06780596,  0.06252882],
             [ 0.05039108,  0.06323181,  0.1004948 ],
             [ 0.03719359,  0.02603368,  0.17122012],
             [-0.01124334,  0.01110709, -0.11718115],
             [ 0.05686841,  0.09495075,  0.10532089],
             [ 0.06037891,  0.07707863,  0.14033521],
             [ 0.05973331,  0.05686997,  0.11341797],
             [ 0.03254955,  0.04815577,  0.01312942],
             [ 0.01776771,  0.02642016, -0.04138332],
             [ 0.02129115,  0.02810647,  0.00106907],
             [ 0.0173785 ,  0.03995643, -0.02388277],
             [ 0.01348561,  0.03692704, -0.03381831],
             [ 0.03912484,  0.03581437,  0.06290846],
             [ 0.00767586,  0.00689587,  0.04550277],
             [-0.06164377, -0.074563  , -0.09811202],
             [ 0.11036201,  0.16693706,  0.16198002]])

    • obs_Ireland
      (obs_Ireland_dim_0, obs_Ireland_dim_1)
      float64
      0.04613 0.06834 ... 0.05461 -0.4713

      array([[ 4.61335791e-02,  6.83401168e-02,  1.49827877e-01],
             [ 4.17197937e-02,  3.04159061e-02, -1.23475797e-01],
             [ 5.50244419e-02,  2.79099604e-02, -3.67648540e-02],
             [ 1.38516968e-02,  2.73181945e-02,  1.27133693e-01],
             [ 7.89156239e-02,  5.36218161e-02,  3.97563116e-02],
             [ 6.94022552e-02,  8.43370255e-02,  1.72927194e-01],
             [ 3.02676413e-02,  4.37312685e-02,  1.27614771e-01],
             [ 3.03286863e-02,  2.12696323e-02, -4.83238754e-02],
             [ 3.27112701e-02,  1.31993486e-02,  9.10272102e-02],
             [ 2.25778666e-02, -4.39091504e-02, -3.47189705e-02],
             [-2.44598876e-03,  4.98375959e-03, -9.74500134e-02],
             [ 4.26223474e-02,  1.22650316e-02, -2.54792846e-02],
             [ 3.03896656e-02,  3.74100113e-02, -8.02856927e-02],
             [-4.29250459e-03,  2.15774944e-02, -2.83320698e-02],
             [ 4.55763509e-02,  1.05522680e-02, -1.14438996e-02],
             [ 5.08586344e-02,  1.99640927e-02,  5.10270372e-02],
             [ 5.65118802e-02,  4.52213918e-02,  9.65358392e-02],
             [ 8.12714443e-02,  2.30526508e-02,  1.25768983e-01],
             [ 1.91125787e-02,  1.99200071e-02, -7.23979883e-02],
             [ 3.28860205e-02,  2.86514636e-02, -2.66017423e-04],
      ...
             [ 5.72894826e-02,  4.32476634e-02,  5.40679052e-02],
             [ 2.96518496e-02,  2.80611431e-02,  7.67303647e-02],
             [ 6.56554548e-02,  3.20210217e-02,  9.31065883e-02],
             [ 5.57772353e-02,  6.12369062e-02,  1.55613972e-01],
             [ 4.86044518e-02,  5.79752697e-02,  6.96325136e-02],
             [ 5.16951629e-02,  6.43787433e-02,  3.09831703e-04],
             [-4.59036270e-02,  3.56558699e-03, -1.23095127e-01],
             [-5.23514448e-02, -4.74316447e-02, -1.85459413e-01],
             [ 1.73985707e-02, -1.16089566e-02, -1.62875961e-01],
             [ 1.06285825e-02,  2.62454869e-03, -1.38828831e-03],
             [-5.23684952e-04, -1.71380002e-02,  1.49189678e-01],
             [ 1.25905519e-02, -1.63944405e-03, -4.22632230e-02],
             [ 8.35476150e-02,  2.97670828e-02,  1.70091250e-01],
             [ 2.24552520e-01,  2.97041623e-02,  4.09453854e-01],
             [ 2.02165860e-02,  4.80931056e-02,  4.07069746e-01],
             [ 8.56272032e-02,  2.60816736e-02, -5.84910067e-03],
             [ 8.64543653e-02,  4.07380268e-02, -9.28996410e-02],
             [ 4.79994419e-02,  4.13795569e-02,  6.90712155e-01],
             [ 5.70131720e-02, -5.33555938e-02, -2.60193601e-01],
             [ 1.26444598e-01,  5.46082354e-02, -4.71301047e-01]])

    • obs_New Zealand
      (obs_New Zealand_dim_0, obs_New Zealand_dim_1)
      float64
      0.01276 0.0003994 ... -0.04888

      array([[ 0.01275757,  0.00039945,  0.05562552],
             [ 0.04550785,  0.01973033,  0.16965206],
             [ 0.00925395, -0.00913711,  0.05374564],
             [ 0.03432179,  0.02948118,  0.09586059],
             [ 0.04681983,  0.03295578,  0.07206984],
             [ 0.01602514,  0.0141673 ,  0.08313887],
             [ 0.02669465,  0.03190073,  0.00063869],
             [ 0.00965985,  0.02347439,  0.05223172],
             [-0.00354805,  0.02166055, -0.01767435],
             [ 0.00161108,  0.02154704,  0.04673256],
             [ 0.00152856,  0.0069469 , -0.03406895],
             [-0.01096479, -0.01994773, -0.16585547],
             [ 0.01088486,  0.00573841,  0.02677066],
             [ 0.06195639,  0.03040616,  0.15858095],
             [ 0.0499192 ,  0.04561174,  0.14225122],
             [ 0.04614348,  0.04011437,  0.08992779],
             [ 0.03551665,  0.04009712,  0.04693239],
             [ 0.02029111,  0.02765009,  0.04662608],
             [ 0.00794279,  0.02562678, -0.06359527],
             [ 0.05307744,  0.02760857,  0.12767563],
      ...
             [ 0.0340567 ,  0.03040034,  0.08290577],
             [ 0.04568639,  0.04065663,  0.07679202],
             [ 0.04449519,  0.05630502,  0.1349896 ],
             [ 0.03949282,  0.05023121,  0.07825136],
             [ 0.03266772,  0.05004526,  0.05561569],
             [ 0.0284034 ,  0.03121604, -0.01671832],
             [ 0.02983217,  0.03945121,  0.07489517],
             [-0.01117747,  0.005312  , -0.07399979],
             [-0.00135262,  0.00921378, -0.10590376],
             [ 0.01512383,  0.02096096,  0.03688958],
             [ 0.02226781,  0.0277072 ,  0.05837884],
             [ 0.02220467,  0.01657869,  0.05313663],
             [ 0.0265973 ,  0.03295962,  0.09054234],
             [ 0.0374444 ,  0.03158895,  0.07775609],
             [ 0.03675934,  0.0366383 ,  0.03531498],
             [ 0.03698213,  0.05200807,  0.02186305],
             [ 0.03515745,  0.04454498,  0.06703786],
             [ 0.0330403 ,  0.04194925,  0.05071202],
             [ 0.02168788,  0.03128527,  0.02580023],
             [-0.01260577,  0.02029054, -0.04887683]])

    • obs_South Africa
      (obs_South Africa_dim_0, obs_South Africa_dim_1)
      float64
      0.04471 0.06648 ... 0.04268 0.02013

      array([[ 4.47051150e-02,  6.64754513e-02,  5.09040274e-02],
             [ 5.93166808e-02,  5.62608597e-02,  6.32529762e-02],
             [ 1.68122171e-02,  5.35913552e-02,  9.31032193e-02],
             [ 2.22492430e-02,  2.46847875e-02, -1.24324541e-02],
             [-9.40233042e-04,  2.68428795e-03, -6.14687390e-02],
             [ 2.96993727e-02,  1.38764596e-02, -2.81211227e-02],
             [ 3.72044440e-02,  3.00933311e-02,  4.08383585e-02],
             [ 6.41063974e-02,  8.36294473e-02,  1.57666347e-01],
             [ 5.22203796e-02,  5.76052512e-02,  8.57594849e-02],
             [-3.84156044e-03,  3.08210094e-02, -2.17288418e-02],
             [-1.86381945e-02,  2.66908702e-02, -3.60537389e-02],
             [ 4.97340198e-02,  5.01916489e-02, -1.50071858e-02],
             [-1.21893986e-02, -1.72244869e-02, -7.28525477e-02],
             [ 1.78476474e-04,  7.25430820e-03, -2.05487765e-01],
             [ 2.07896794e-02,  3.75301356e-02, -5.25230432e-02],
             [ 4.11429956e-02,  4.23097973e-02,  1.18525664e-01],
             [ 2.36656964e-02,  3.03063946e-02,  6.30169602e-02],
             [-3.18266357e-03,  2.67459923e-02, -2.36844273e-02],
             [-1.02346454e-02,  2.19137613e-03, -7.67546375e-02],
             [-2.16019802e-02, -5.34858092e-03, -5.40315019e-02],
      ...
             [ 3.63355397e-02,  3.43620535e-02,  3.43300225e-02],
             [ 2.90642670e-02,  3.43103698e-02,  9.74625263e-02],
             [ 4.45388535e-02,  5.82814840e-02,  1.21128375e-01],
             [ 5.14252794e-02,  4.81903464e-02,  1.04213487e-01],
             [ 5.45242306e-02,  7.35687362e-02,  1.14619392e-01],
             [ 5.22173708e-02,  6.24956095e-02,  1.28909455e-01],
             [ 3.14118792e-02,  2.59384473e-02,  1.20645751e-01],
             [-1.55004043e-02, -1.60128132e-02, -6.91009142e-02],
             [ 2.99444840e-02,  4.17842195e-02, -3.99083704e-02],
             [ 3.11939334e-02,  3.98013850e-02,  6.61950516e-02],
             [ 2.36797328e-02,  3.51947516e-02,  1.74217409e-02],
             [ 2.45508270e-02,  1.90371107e-02,  5.21926438e-02],
             [ 1.40392514e-02,  9.96208252e-03, -1.32604270e-02],
             [ 1.31320187e-02,  1.41410543e-02,  1.34055579e-02],
             [ 6.62353893e-03,  9.84260750e-03, -1.95087200e-02],
             [ 1.15129405e-02,  1.24423566e-02, -2.05408909e-02],
             [ 1.47666087e-02,  2.05234972e-02, -1.78043515e-02],
             [ 1.12989839e-03,  1.42409638e-02, -2.44166814e-02],
             [-6.64814723e-02, -4.82250860e-02, -1.61237297e-01],
             [ 4.79765253e-02,  4.26787540e-02,  2.01288685e-02]])

    • obs_United Kingdom
      (obs_United Kingdom_dim_0, obs_United Kingdom_dim_1)
      float64
      0.0632 0.04994 ... 0.07793 0.05719

      array([[ 0.0631987 ,  0.04994497,  0.06337169],
             [-0.02515786, -0.00812863, -0.01970066],
             [-0.01484616,  0.01383284, -0.01909747],
             [ 0.02868722,  0.00806818,  0.01712351],
             [ 0.02428034, -0.00627614, -0.01543497],
             [ 0.04118283,  0.04299063,  0.0248173 ],
             [ 0.03680449,  0.03551332,  0.02585783],
             [-0.02052284,  0.00363682, -0.04865774],
             [-0.00790863,  0.00178865, -0.0913653 ],
             [ 0.01975254,  0.00986482,  0.05837711],
             [ 0.04135167,  0.03471082,  0.04922731],
             [ 0.02243744,  0.0200251 ,  0.08704313],
             [ 0.04063716,  0.0272396 ,  0.04084613],
             [ 0.03101735,  0.05030823,  0.02170983],
             [ 0.05252355,  0.04003375,  0.0905554 ],
             [ 0.05574132,  0.05698841,  0.13841338],
             [ 0.02544943,  0.02841384,  0.05919042],
             [ 0.00731077,  0.01256388, -0.02235462],
             [-0.01109251, -0.00849372, -0.06537815],
             [ 0.0040028 ,  0.01360378,  0.00895118],
      ...
             [ 0.02100996,  0.03285221,  0.02787326],
             [ 0.02984895,  0.03346377,  0.02706516],
             [ 0.02328313,  0.03152612,  0.02325109],
             [ 0.02560225,  0.02491369,  0.04169183],
             [ 0.02551281,  0.01679235,  0.0267212 ],
             [ 0.02244117,  0.01937612,  0.04536821],
             [-0.00239926,  0.00310638, -0.03581101],
             [-0.04340195, -0.01724746, -0.13593041],
             [ 0.02109041,  0.01300281,  0.03628414],
             [ 0.01447043,  0.00184942,  0.00570219],
             [ 0.01459189,  0.01615877,  0.01511258],
             [ 0.01872379,  0.01716657,  0.03228887],
             [ 0.02947302,  0.02440921,  0.06598913],
             [ 0.02588796,  0.03009682,  0.06147314],
             [ 0.02238227,  0.02906562,  0.04613987],
             [ 0.02111993,  0.01376355,  0.03244003],
             [ 0.01637446,  0.01897499, -0.00063386],
             [ 0.01658121,  0.01894308,  0.00545265],
             [-0.09728665, -0.09991479, -0.09989816],
             [ 0.07177422,  0.07792672,  0.05718545]])

    • obs_United States
      (obs_United States_dim_0, obs_United States_dim_1)
      float64
      -0.002057 0.0228 ... -0.01562

      array([[-0.00205667,  0.02279784, -0.07580306],
             [ 0.05247991,  0.0423446 ,  0.07725835],
             [ 0.04520425,  0.0363257 ,  0.09829596],
             [ 0.05387536,  0.03756695,  0.10123019],
             [ 0.03117056,  0.02023809,  0.05542428],
             [-0.0025708 ,  0.00055427, -0.04387308],
             [ 0.02506054,  0.01420906,  0.01889814],
             [-0.01819337,  0.01631303, -0.05093106],
             [ 0.04481956,  0.04978586,  0.07007873],
             [ 0.06986773,  0.04381145,  0.139842  ],
             [ 0.04085069,  0.04976591,  0.06770261],
             [ 0.03404045,  0.04134896,  0.03097407],
             [ 0.03400765,  0.03055211,  0.01752661],
             [ 0.04092178,  0.03667373,  0.02285645],
             [ 0.03606814,  0.02904549,  0.02888397],
             [ 0.01868401,  0.02135529, -0.00104886],
             [-0.00108323,  0.00492023, -0.04193738],
             [ 0.03461822,  0.03016452,  0.04018221],
             [ 0.027146  ,  0.02738892,  0.04969453],
             [ 0.03949753,  0.03169813,  0.05925663],
      ...
             [ 0.00949814,  0.02632002, -0.00424008],
             [ 0.01681722,  0.02737844, -0.01710235],
             [ 0.02757829,  0.02855487,  0.04149606],
             [ 0.03780194,  0.03301059,  0.05820109],
             [ 0.03423929,  0.0299518 ,  0.058829  ],
             [ 0.02744794,  0.02555851,  0.02639172],
             [ 0.01990564,  0.02252906, -0.00580617],
             [ 0.00122114,  0.00574324, -0.04296584],
             [-0.02634283, -0.00251815, -0.1337838 ],
             [ 0.02672817,  0.01518253,  0.02207697],
             [ 0.01538007,  0.00758364,  0.0447487 ],
             [ 0.02255069,  0.00827521,  0.06644212],
             [ 0.01825118,  0.00854824,  0.03506226],
             [ 0.02261999,  0.02050827,  0.05006005],
             [ 0.02670395,  0.02934843,  0.03586364],
             [ 0.01653722,  0.02342548,  0.02105755],
             [ 0.02230616,  0.01988538,  0.03747989],
             [ 0.02877069,  0.02565042,  0.04277978],
             [ 0.02263068,  0.02139597,  0.03075832],
             [-0.03463896, -0.028277  , -0.01561854]])

  • Indexes: (16)
    • obs_Australia_dim_0
      PandasIndex

      PandasIndex(Int64Index([ 0,  1,  2,  3,  4,  5,  6,  7,  8,  9, 10, 11, 12, 13, 14, 15, 16,
                  17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33,
                  34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48],
                 dtype='int64', name='obs_Australia_dim_0'))

    • obs_Australia_dim_1
      PandasIndex

      PandasIndex(Int64Index([0, 1, 2], dtype='int64', name='obs_Australia_dim_1'))

    • obs_Canada_dim_0
      PandasIndex

      PandasIndex(Int64Index([0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18,
                  19, 20, 21],
                 dtype='int64', name='obs_Canada_dim_0'))

    • obs_Canada_dim_1
      PandasIndex

      PandasIndex(Int64Index([0, 1, 2], dtype='int64', name='obs_Canada_dim_1'))

    • obs_Chile_dim_0
      PandasIndex

      PandasIndex(Int64Index([ 0,  1,  2,  3,  4,  5,  6,  7,  8,  9, 10, 11, 12, 13, 14, 15, 16,
                  17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33,
                  34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48],
                 dtype='int64', name='obs_Chile_dim_0'))

    • obs_Chile_dim_1
      PandasIndex

      PandasIndex(Int64Index([0, 1, 2], dtype='int64', name='obs_Chile_dim_1'))

    • obs_Ireland_dim_0
      PandasIndex

      PandasIndex(Int64Index([ 0,  1,  2,  3,  4,  5,  6,  7,  8,  9, 10, 11, 12, 13, 14, 15, 16,
                  17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33,
                  34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48],
                 dtype='int64', name='obs_Ireland_dim_0'))

    • obs_Ireland_dim_1
      PandasIndex

      PandasIndex(Int64Index([0, 1, 2], dtype='int64', name='obs_Ireland_dim_1'))

    • obs_New Zealand_dim_0
      PandasIndex

      PandasIndex(Int64Index([ 0,  1,  2,  3,  4,  5,  6,  7,  8,  9, 10, 11, 12, 13, 14, 15, 16,
                  17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33,
                  34, 35, 36, 37, 38, 39, 40],
                 dtype='int64', name='obs_New Zealand_dim_0'))

    • obs_New Zealand_dim_1
      PandasIndex

      PandasIndex(Int64Index([0, 1, 2], dtype='int64', name='obs_New Zealand_dim_1'))

    • obs_South Africa_dim_0
      PandasIndex

      PandasIndex(Int64Index([ 0,  1,  2,  3,  4,  5,  6,  7,  8,  9, 10, 11, 12, 13, 14, 15, 16,
                  17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33,
                  34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48],
                 dtype='int64', name='obs_South Africa_dim_0'))

    • obs_South Africa_dim_1
      PandasIndex

      PandasIndex(Int64Index([0, 1, 2], dtype='int64', name='obs_South Africa_dim_1'))

    • obs_United Kingdom_dim_0
      PandasIndex

      PandasIndex(Int64Index([ 0,  1,  2,  3,  4,  5,  6,  7,  8,  9, 10, 11, 12, 13, 14, 15, 16,
                  17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33,
                  34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48],
                 dtype='int64', name='obs_United Kingdom_dim_0'))

    • obs_United Kingdom_dim_1
      PandasIndex

      PandasIndex(Int64Index([0, 1, 2], dtype='int64', name='obs_United Kingdom_dim_1'))

    • obs_United States_dim_0
      PandasIndex

      PandasIndex(Int64Index([ 0,  1,  2,  3,  4,  5,  6,  7,  8,  9, 10, 11, 12, 13, 14, 15, 16,
                  17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33,
                  34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45],
                 dtype='int64', name='obs_United States_dim_0'))

    • obs_United States_dim_1
      PandasIndex

      PandasIndex(Int64Index([0, 1, 2], dtype='int64', name='obs_United States_dim_1'))

  • Attributes: (4)

    created_at :

    2023-02-21T19:22:35.401625

    arviz_version :

    0.14.0

    inference_library :

    pymc

    inference_library_version :

    5.0.1

  
  

az.plot_trace(
    idata_full_test,
    var_names=["rho", "alpha_hat_location", "beta_hat_location", "omega_global"],
    kind="rank_vlines",
);

Next we'll look at some of the summary statistics and how they vary across the countries.

az.summary(
    idata_full_test,
    var_names=[
        "rho",
        "alpha_hat_location",
        "alpha_hat_scale",
        "beta_hat_location",
        "beta_hat_scale",
        "z_scale_alpha_Ireland",
        "z_scale_alpha_United States",
        "z_scale_beta_Ireland",
        "z_scale_beta_United States",
        "alpha_Ireland",
        "alpha_United States",
        "omega_global_corr",
        "lag_coefs_Ireland",
        "lag_coefs_United States",
    ],
)

/Users/nathanielforde/mambaforge/envs/myjlabenv/lib/python3.11/site-packages/arviz/stats/diagnostics.py:584: RuntimeWarning: invalid value encountered in scalar divide
  (between_chain_variance / within_chain_variance + num_samples - 1) / (num_samples)

	mean	sd	hdi_3%	hdi_97%	mcse_mean	mcse_sd	ess_bulk	ess_tail	r_hat
rho	0.974	0.006	0.962	0.984	0.000	0.000	749.0	1354.0	1.00
alpha_hat_location	0.022	0.002	0.018	0.026	0.000	0.000	1642.0	3651.0	1.00
alpha_hat_scale	0.047	0.012	0.027	0.069	0.000	0.000	2933.0	1097.0	1.00
beta_hat_location	0.029	0.009	0.014	0.046	0.000	0.000	855.0	2218.0	1.00
beta_hat_scale	0.186	0.064	0.077	0.305	0.003	0.002	312.0	647.0	1.01
z_scale_alpha_Ireland	0.264	0.147	0.070	0.508	0.002	0.002	2074.0	854.0	1.00
z_scale_alpha_United States	0.132	0.066	0.045	0.245	0.001	0.001	8457.0	5680.0	1.00
z_scale_beta_Ireland	0.508	0.326	0.096	1.067	0.014	0.010	592.0	1294.0	1.00
z_scale_beta_United States	0.213	0.125	0.050	0.445	0.005	0.003	646.0	1423.0	1.00
alpha_Ireland[dl_gdp]	0.035	0.008	0.020	0.048	0.000	0.000	3446.0	4001.0	1.00
alpha_Ireland[dl_cons]	0.014	0.006	0.003	0.024	0.000	0.000	1597.0	4464.0	1.00
alpha_Ireland[dl_gfcf]	0.024	0.011	0.002	0.046	0.000	0.000	6768.0	5217.0	1.00
alpha_United States[dl_gdp]	0.021	0.003	0.015	0.026	0.000	0.000	2322.0	3773.0	1.00
alpha_United States[dl_cons]	0.020	0.003	0.015	0.025	0.000	0.000	2164.0	3321.0	1.00
alpha_United States[dl_gfcf]	0.024	0.005	0.015	0.034	0.000	0.000	4455.0	5176.0	1.00
omega_global_corr[0, 0]	1.000	0.000	1.000	1.000	0.000	0.000	8000.0	8000.0	NaN
omega_global_corr[0, 1]	0.980	0.019	0.944	1.000	0.000	0.000	2393.0	2273.0	1.00
omega_global_corr[0, 2]	0.916	0.033	0.854	0.977	0.001	0.001	915.0	763.0	1.00
omega_global_corr[1, 0]	0.980	0.019	0.944	1.000	0.000	0.000	2393.0	2273.0	1.00
omega_global_corr[1, 1]	1.000	0.000	1.000	1.000	0.000	0.000	7937.0	7898.0	1.00
omega_global_corr[1, 2]	0.879	0.045	0.794	0.960	0.001	0.001	1345.0	3018.0	1.00
omega_global_corr[2, 0]	0.916	0.033	0.854	0.977	0.001	0.001	915.0	763.0	1.00
omega_global_corr[2, 1]	0.879	0.045	0.794	0.960	0.001	0.001	1345.0	3018.0	1.00
omega_global_corr[2, 2]	1.000	0.000	1.000	1.000	0.000	0.000	8042.0	7890.0	1.00
lag_coefs_Ireland[dl_gdp, 1, dl_gdp]	0.012	0.080	-0.151	0.160	0.001	0.001	5559.0	3646.0	1.00
lag_coefs_Ireland[dl_gdp, 1, dl_cons]	0.007	0.086	-0.161	0.174	0.001	0.002	4661.0	3294.0	1.00
lag_coefs_Ireland[dl_gdp, 1, dl_gfcf]	0.057	0.037	-0.009	0.128	0.001	0.000	4699.0	4249.0	1.00
lag_coefs_Ireland[dl_gdp, 2, dl_gdp]	-0.005	0.087	-0.176	0.152	0.002	0.002	3099.0	2447.0	1.00
lag_coefs_Ireland[dl_gdp, 2, dl_cons]	0.003	0.088	-0.171	0.171	0.001	0.001	4239.0	2997.0	1.00
lag_coefs_Ireland[dl_gdp, 2, dl_gfcf]	0.104	0.041	0.027	0.180	0.001	0.001	1785.0	4172.0	1.00
lag_coefs_Ireland[dl_cons, 1, dl_gdp]	0.132	0.081	-0.000	0.287	0.002	0.002	1109.0	1022.0	1.00
lag_coefs_Ireland[dl_cons, 1, dl_cons]	0.158	0.110	-0.004	0.376	0.003	0.002	1227.0	2390.0	1.00
lag_coefs_Ireland[dl_cons, 1, dl_gfcf]	-0.031	0.028	-0.082	0.023	0.001	0.000	1756.0	4031.0	1.00
lag_coefs_Ireland[dl_cons, 2, dl_gdp]	0.018	0.069	-0.120	0.147	0.001	0.001	5040.0	3039.0	1.00
lag_coefs_Ireland[dl_cons, 2, dl_cons]	0.048	0.073	-0.095	0.189	0.001	0.001	5765.0	3448.0	1.00
lag_coefs_Ireland[dl_cons, 2, dl_gfcf]	0.071	0.025	0.021	0.116	0.000	0.000	5169.0	5742.0	1.00
lag_coefs_Ireland[dl_gfcf, 1, dl_gdp]	0.091	0.118	-0.094	0.332	0.003	0.002	2232.0	1385.0	1.00
lag_coefs_Ireland[dl_gfcf, 1, dl_cons]	0.058	0.099	-0.136	0.254	0.002	0.002	5377.0	2440.0	1.00
lag_coefs_Ireland[dl_gfcf, 1, dl_gfcf]	0.064	0.076	-0.076	0.216	0.001	0.001	4693.0	3703.0	1.00
lag_coefs_Ireland[dl_gfcf, 2, dl_gdp]	0.050	0.092	-0.121	0.232	0.001	0.001	6475.0	3196.0	1.00
lag_coefs_Ireland[dl_gfcf, 2, dl_cons]	0.024	0.096	-0.154	0.221	0.001	0.002	5052.0	3012.0	1.00
lag_coefs_Ireland[dl_gfcf, 2, dl_gfcf]	-0.048	0.093	-0.239	0.102	0.002	0.002	1904.0	2237.0	1.00
lag_coefs_United States[dl_gdp, 1, dl_gdp]	0.033	0.044	-0.043	0.122	0.001	0.001	2364.0	1396.0	1.00
lag_coefs_United States[dl_gdp, 1, dl_cons]	0.031	0.042	-0.044	0.119	0.001	0.001	3946.0	2353.0	1.00
lag_coefs_United States[dl_gdp, 1, dl_gfcf]	-0.008	0.031	-0.072	0.043	0.001	0.001	1330.0	2254.0	1.00
lag_coefs_United States[dl_gdp, 2, dl_gdp]	0.036	0.042	-0.037	0.121	0.001	0.001	3903.0	2216.0	1.00
lag_coefs_United States[dl_gdp, 2, dl_cons]	0.048	0.047	-0.033	0.141	0.001	0.001	1335.0	1481.0	1.00
lag_coefs_United States[dl_gdp, 2, dl_gfcf]	0.027	0.028	-0.027	0.076	0.000	0.000	3760.0	1877.0	1.00
lag_coefs_United States[dl_cons, 1, dl_gdp]	0.024	0.041	-0.060	0.102	0.001	0.001	5468.0	2430.0	1.00
lag_coefs_United States[dl_cons, 1, dl_cons]	0.044	0.047	-0.031	0.141	0.001	0.001	1768.0	1738.0	1.00
lag_coefs_United States[dl_cons, 1, dl_gfcf]	0.007	0.031	-0.053	0.060	0.001	0.001	1909.0	2312.0	1.00
lag_coefs_United States[dl_cons, 2, dl_gdp]	0.039	0.044	-0.033	0.131	0.001	0.001	2644.0	1843.0	1.00
lag_coefs_United States[dl_cons, 2, dl_cons]	0.036	0.042	-0.040	0.116	0.001	0.001	4171.0	1978.0	1.00
lag_coefs_United States[dl_cons, 2, dl_gfcf]	0.031	0.027	-0.018	0.084	0.000	0.000	4192.0	2149.0	1.00
lag_coefs_United States[dl_gfcf, 1, dl_gdp]	0.039	0.045	-0.045	0.129	0.001	0.001	3809.0	1798.0	1.00
lag_coefs_United States[dl_gfcf, 1, dl_cons]	0.034	0.045	-0.046	0.125	0.001	0.001	4896.0	2476.0	1.00
lag_coefs_United States[dl_gfcf, 1, dl_gfcf]	0.075	0.057	-0.005	0.189	0.002	0.002	746.0	1317.0	1.00
lag_coefs_United States[dl_gfcf, 2, dl_gdp]	0.016	0.047	-0.078	0.102	0.001	0.001	4171.0	1975.0	1.00
lag_coefs_United States[dl_gfcf, 2, dl_cons]	0.018	0.047	-0.078	0.104	0.001	0.001	4508.0	1892.0	1.00
lag_coefs_United States[dl_gfcf, 2, dl_gfcf]	0.015	0.043	-0.072	0.091	0.001	0.001	2937.0	2034.0	1.00

ax = az.plot_forest(
    idata_full_test,
    var_names=[
        "alpha_Ireland",
        "alpha_United States",
        "alpha_Australia",
        "alpha_Chile",
        "alpha_New Zealand",
        "alpha_South Africa",
        "alpha_Canada",
        "alpha_United Kingdom",
    ],
    kind="ridgeplot",
    combined=True,
    ridgeplot_truncate=False,
    ridgeplot_quantiles=[0.25, 0.5, 0.75],
    ridgeplot_overlap=0.7,
    figsize=(10, 10),
)

ax[0].axvline(0, color="red")
ax[0].set_title("Intercept Parameters for each country \n and Economic Measure");

ax = az.plot_forest(
    idata_full_test,
    var_names=[
        "lag_coefs_Ireland",
        "lag_coefs_United States",
        "lag_coefs_Australia",
        "lag_coefs_Chile",
        "lag_coefs_New Zealand",
        "lag_coefs_South Africa",
        "lag_coefs_Canada",
        "lag_coefs_United Kingdom",
    ],
    kind="ridgeplot",
    ridgeplot_truncate=False,
    figsize=(10, 10),
    coords={"equations": "dl_cons", "lags": 1, "cross_vars": "dl_gdp"},
)
ax[0].axvline(0, color="red")
ax[0].set_title("Lag Coefficient for the first lag of GDP on Consumption \n by Country");

Next we'll examine the correlation between the three variables and see what we've learned by including the hierarchical structure.

corr = pd.DataFrame(
    az.summary(idata_full_test, var_names=["omega_global_corr"])["mean"].values.reshape(3, 3),
    columns=["GDP", "CONS", "GFCF"],
)
corr.index = ["GDP", "CONS", "GFCF"]
corr

/Users/nathanielforde/mambaforge/envs/myjlabenv/lib/python3.11/site-packages/arviz/stats/diagnostics.py:584: RuntimeWarning: invalid value encountered in scalar divide
  (between_chain_variance / within_chain_variance + num_samples - 1) / (num_samples)

	GDP	CONS	GFCF
GDP	1.000	0.980	0.916
CONS	0.980	1.000	0.879
GFCF	0.916	0.879	1.000

ax = az.plot_posterior(
    idata_full_test,
    var_names="omega_global_corr",
    hdi_prob="hide",
    point_estimate="mean",
    grid=(3, 3),
    kind="hist",
    ec="black",
    figsize=(10, 7),
)
titles = [
    "GDP/GDP",
    "GDP/CONS",
    "GDP/GFCF",
    "CONS/GDP",
    "CONS/CONS",
    "CONS/GFCF",
    "GFCF/GDP",
    "GFCF/CONS",
    "GFCF/GFCF",
]
for ax, t in zip(ax.ravel(), titles):
    ax.set_xlim(0.6, 1)
    ax.set_title(t, fontsize=10)
plt.suptitle("The Posterior Correlation Estimates", fontsize=20);

We can see these estimates of the correlations between the 3 economic variables differ markedly from the simple case where we examined Ireland alone. In particular we can see that the correlation between GDF and CONS is now much higher. Which suggests that we have learned something about the relationship between these variables which would not be clear examining the Irish case alone.

Next we'll plot the model fits for each country to ensure that the predictive distribution can recover the observed data. It is important for the question of model adequacy that we can recover both the outlier case of Ireland and the more regular countries such as Australia and United States.

az.plot_ppc(idata_full_test);

And to see the development of these model fits over time:

countries = gdp_hierarchical["country"].unique()


fig, axs = plt.subplots(8, 3, figsize=(20, 40))
for ax, country in zip(axs, countries):
    temp = pd.DataFrame(
        idata_full_test["observed_data"][f"obs_{country}"].data,
        columns=["dl_gdp", "dl_cons", "dl_gfcf"],
    )
    ppc = az.extract(idata_full_test, group="posterior_predictive", num_samples=100)[
        f"obs_{country}"
    ]
    if country == "Ireland":
        color = "viridis"
    else:
        color = "inferno"
    for i in range(3):
        shade_background(ppc, ax, i, color)
    ax[0].plot(np.arange(ppc.shape[0]), ppc[:, 0, :].mean(axis=1), color="cyan", label="Mean")
    ax[0].plot(temp["dl_gdp"], "o", mfc="black", mec="white", mew=1, markersize=7, label="Observed")
    ax[0].set_title(f"Posterior Predictive GDP: {country}")
    ax[0].legend(loc="lower left")
    ax[1].plot(
        temp["dl_cons"], "o", mfc="black", mec="white", mew=1, markersize=7, label="Observed"
    )
    ax[1].plot(np.arange(ppc.shape[0]), ppc[:, 1, :].mean(axis=1), color="cyan", label="Mean")
    ax[1].set_title(f"Posterior Predictive Consumption: {country}")
    ax[1].legend(loc="lower left")
    ax[2].plot(
        temp["dl_gfcf"], "o", mfc="black", mec="white", mew=1, markersize=7, label="Observed"
    )
    ax[2].plot(np.arange(ppc.shape[0]), ppc[:, 2, :].mean(axis=1), color="cyan", label="Mean")
    ax[2].set_title(f"Posterior Predictive Investment: {country}")
    ax[2].legend(loc="lower left")
plt.suptitle("Posterior Predictive Checks on Hierarchical VAR", fontsize=20);

Here we can see that the model appears to have recovered reasonable posterior predictions for the observed data and the volatility of the Irish GDP figures is clear next to the other countries. Whether this is a cautionary tale about data quality or the corruption of metrics we leave to the economists to figure out.

Conclusion

VAR modelling is a rich an interesting area of research within economics and there are a range of challenges and pitfalls which come with the interpretation and understanding of these models. We hope this example encourages you to continue exploring the potential of this kind of VAR modelling in the Bayesian framework. Whether you're interested in the relationship between grand economic theory or simpler questions about the impact of poor app performance on customer feedback, VAR models give you a powerful tool for interrogating these relationships over time. As we've seen Hierarchical VARs further enables the precise quantification of outliers within a cohort and does not throw away the information because of odd accounting practices engendered by international capitalism.

In the next post in this series we will spend some time digging into the implied relationships between the timeseries which result from fitting our VAR models.

References

:::{bibliography} :filter: docname in docnames :::

Authors

• Adapted from the PYMC labs Blog post and Jim Savage's discussion here by Nathaniel Forde in November 2022 (pymc-examples#456)
• Reexecuted by Nathaniel Forde on Feb, 2023 (pymc_examples#523)

Watermark

%load_ext watermark
%watermark -n -u -v -iv -w -p pytensor,aeppl,xarray

Last updated: Tue Feb 21 2023

Python implementation: CPython
Python version       : 3.11.0
IPython version      : 8.9.0

pytensor: 2.8.11
aeppl   : not installed
xarray  : 2023.1.0

pymc       : 5.0.1
statsmodels: 0.13.5
pandas     : 1.5.3
numpy      : 1.24.1
matplotlib : 3.6.3
arviz      : 0.14.0

Watermark: 2.3.1

:::{include} ../page_footer.md :::