GibbsBVARResult#

class cultivars.multivariate.large_dim.gibbs.GibbsBVARResult(*, endog, names, order, trend, prior_label, coefficients, deterministic, beta_mean, sigma_u, beta_draws, sigma_draws, shrinkage, shrinkage_label, resid, fittedvalues, nobs, n_dummy, n_draws, n_burn, thin, _engine)[source]

Bases: _VectorPosteriorDrawsResult

A fitted Gibbs BVAR: a sampled posterior, and the prior’s own diagnostics.

The posterior of

\[y_t = c + \sum_{i=1}^{p} A_i y_{t-i} + u_t, \qquad u_t \sim N(0, \Sigma),\]

under a prior on the stacked coefficients \(\beta\) stated independently of \(\Sigma\), reached by Gibbs sampling: a joint generalized-least-squares draw of \(\beta \mid \Sigma, y\), an inverse-Wishart draw of \(\Sigma \mid \beta, y\), and, under an adaptive prior, one sweep of the scale hierarchy’s conditionals. The propagation surface – credible intervals, impulse responses with posterior bands, the posterior predictive, the stability share, the chain diagnostics – is the family’s shared one from _VectorPosteriorDrawsResult. What this result adds is the adaptive prior’s averaged latent diagnostic – inclusion probabilities under a selection prior, local shrinkage scales under a global-local one – and Chib’s marginal likelihood where the two-block sampler makes it exact.

Note

marginal_likelihood is available under a static moment prior and refused under an adaptive prior (whose scale block would need reduced runs) or a dummy-observation prior (whose artificial rows the sampler treats as data). shrinkage is the posterior mean of the latent diagnostic, Rao-Blackwellized over kept sweeps: a conditional inclusion probability, not a binary indicator, under a selection prior; a conditional prior standard deviation on the standardized scale under a global-local prior. The draws are a Markov chain – burn-in and thinning are real choices and convergence says whether they were enough. The point summaries (coefficients, sigma_u, resid) are at the posterior mean and inherit its caveats.

Variables:

  • prior_label – Short description of the prior estimated under.

  • shrinkage – (w, k) posterior mean per-coefficient diagnostic from an adaptive prior, in design-row order; empty under a static prior. Read it through inclusion_probabilities() or shrinkage_scales().

  • shrinkage_label – What shrinkage is; empty under a static prior.

  • n_dummy – Artificial rows the prior contributed.

  • n_draws – Total sampler iterations.

  • n_burn – Burn-in discarded.

  • thin – Post-burn thinning.

See also

  • GibbsBVAR – the model that produces this record.

  • BVARResult – the conjugate posterior, exact and with a closed-form marginal likelihood.

  • SpikeAndSlabPrior – the selection prior whose inclusion map this result reports.

References

Koop, G., & Korobilis, D. (2010). Bayesian multivariate time series methods for empirical macroeconomics. Foundations and Trends in Econometrics, 3(4), 267-358.

George, E. I., Sun, D., & Ni, S. (2008). Bayesian stochastic search for VAR model restrictions. Journal of Econometrics, 142(1), 553-580.

Chib, S. (1995). Marginal likelihood from the Gibbs output. Journal of the American Statistical Association, 90(432), 1313-1321.

Example

A diagonal VAR(1) under a selection prior: the own lags are included with probability near one and the cross lags are not:

>>> import numpy as np
>>> from cultivars.bayes.priors import SpikeAndSlabPrior
>>> rng = np.random.default_rng(0)
>>> y = np.zeros((200, 3))
>>> for t in range(1, 200):
...     y[t] = 0.6 * y[t - 1] + rng.standard_normal(3)
>>> res = GibbsBVAR(y, order=1, prior=SpikeAndSlabPrior()).fit(
...     n_draws=300, n_burn=100, seed=0
... )
>>> res.prior_label, res.shrinkage_label, res.n_kept, res.n_dummy
('ssvs(spike=0.1, slab=10, p=0.5)', 'posterior inclusion probability', 200, 0)
>>> res.shrinkage.shape, res.beta_draws.shape, res.sigma_draws.shape
((4, 3), (200, 4, 3), (200, 3, 3))
>>> included = res.inclusion_probabilities()[0]
>>> off_diagonal = included[~np.eye(3, dtype=bool)]
>>> bool(np.all(np.diag(included) > 0.9)), bool(off_diagonal.max() < 0.5)
(True, True)
>>> low, mid, high = res.credible_interval("y1", "y1.L1")
>>> bool(0.3 < low < mid < high < 0.8)
True

Private attributes#

_engine

The model, kept for the marginal-likelihood estimator.

Private methods#

_from_fit(fit, model)

Assemble the public result from a raw fit and its specification.

_lag_diagnostic()

The lag-block rows of shrinkage as a (p, k, k) stack.

_summary_table()

Build the structured summary.