GibbsBVARResult.shrinkage_scales#

GibbsBVARResult.shrinkage_scales()[source]#

Posterior mean local-global scale of each standardized lag coefficient.

Entry [lag, i, j] is the averaged prior standard deviation the hierarchy assigned to that coefficient on the standardized (unit-free) scale: near zero means shrunk away, order one means left free. Comparable within a fit, not across priors.

Return type:

NDArray[double]

Returns:

A (p, k, k) stack aligned with coefficients.

Raises:

SpecificationError – If the prior was not a global-local shrinkage prior.

Example

Under the horseshoe the own lags of a diagonal VAR keep a larger scale than the cross lags:

>>> import numpy as np
>>> from cultivars.bayes.priors import HorseshoePrior
>>> 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=HorseshoePrior()).fit(
...     n_draws=300, n_burn=100, seed=0
... )
>>> scale = res.shrinkage_scales()[0]
>>> scale.shape, bool(np.diag(scale).min() > scale[~np.eye(3, dtype=bool)].max())
((3, 3), True)
>>> static = GibbsBVAR(y, order=1).fit(n_draws=60, n_burn=20, seed=0)
>>> static.shrinkage_scales()
Traceback (most recent call last):
cultivars.exceptions.SpecificationError: shrinkage scales exist only under a ...