NaturalConjugate¶

The NaturalConjugate model implements Bayesian VAR estimation with a Natural-Conjugate Normal-Inverse-Wishart prior. Conjugacy gives a closed-form posterior, so the model needs neither MCMC nor burn-in. This makes it a fast and versatile option for most applications.

Constructor arguments (minnesota, soc, sur, covid, covid_dates) are documented on SamplingModel; soc and sur default to True.

Prior Structure¶

The prior is specified jointly over the coefficients and the covariance matrix:

\[\text{vec}(A) \mid \Sigma \,\sim\, \mathcal{N}\!\left(\beta_0,\; \Sigma \otimes V_A^{-1}\right)\]

\[\Sigma \,\sim\, \mathcal{IW}(S_0, \nu_0)\]

where \(V_A^{-1}\) is the \((k \times k)\) per-equation prior precision matrix (Minnesota form) and \(\beta_0\) encodes the random-walk prior means. After observing data \(Y\), the posteriors update to known closed-form distributions, from which draws are taken directly.

Hyperparameters¶

Parameter	Description	Default
`c1`	Overall shrinkage / tightness	0.2
`c3`	Lag-decay exponent	2.0
`mu`	SOC tightness (if `soc=True`)	1.0
`theta`	SUR tightness (if `sur=True`)	1.0
`lambda_covid`	COVID-dummy prior variance	10 000

Hyperparameters can be set manually via set_priors() or optimised automatically with BVAR.optimise_hyperparameters() (uses marginal-likelihood maximisation).

Example¶

import bvar as bv

model = bv.NaturalConjugate(
    minnesota=True,
    soc=True,
    sur=True,
    covid=True,
)

bvar = bv.BVAR(n_lags=4, model=model, stationary=False, optimisation_method="ml")
bvar.optimise_hyperparameters(data)
bvar.sample(data, N_draws=5000)

API¶

bvar.NaturalConjugate ¶

NaturalConjugate(minnesota: bool = True, soc: bool = True, sur: bool = True, covid: bool = False, covid_dates: Optional[list] = None)

BVAR with Natural-Conjugate (Normal-Inverse-Wishart) priors.

The prior is vec(A) | Σ ~ N(β₀, Σ ⊗ V_A⁻¹) and Σ ~ IW(S₀, ν₀). Posterior sampling follows Chan (2020).

ATTRIBUTE	DESCRIPTION
`requires_burnin`	`False` — draws come directly from the known posterior. TYPE: `bool`
`supports_ml`	`True` — a closed-form marginal likelihood is available (GLP 2015). TYPE: `bool`

sample ¶

sample(data: ndarray, n_lags: int, covid_indices: ndarray, vars_in_levels: ndarray, N_draws: int, point_only: bool = False, progressbar: bool = True, soc: Optional[bool] = None, sur: Optional[bool] = None, rng: Optional[Generator] = None) -> SamplingResult

Run the full conjugate estimation pipeline.

sample_posterior_state ¶

sample_posterior_state(Y: ndarray, Z: ndarray, current_state: PosteriorState, rng: Optional[Generator] = None) -> PosteriorState

Return a single random posterior draw as a PosteriorState.

Draws one sample from the known Normal-Inverse-Wishart posterior using the stored prior (self.beta_0, self.V_A_inv, self.pars.S_0, self.pars.nu_0) from the last call to :meth:sample. The method accepts current_state for interface compatibility but ignores it because the posterior comes directly from the closed-form distribution rather than an MCMC update.