MinnesotaPrior

class impulso.priors.MinnesotaPrior(*, tightness=0.1, decay='harmonic', cross_shrinkage=0.5)

Bases: ImpulsoModel

Minnesota prior for VAR coefficient shrinkage.

tightness is always held fixed at the value supplied; there is no estimation path for it. That is the deliberate contrast with NIWPrior, whose select flag estimates the tightness by marginal likelihood — the independent-Normal coefficient prior used here has no closed-form marginal likelihood to maximise, so the shrinkage stays a modelling choice rather than an estimand.

Parameters:

• tightness (Annotated[float, Gt(gt=0)])

• decay (Literal['harmonic', 'geometric'])

• cross_shrinkage (Annotated[float, Ge(ge=0), Le(le=1)])

tightness

Overall shrinkage toward prior mean. Must be > 0. Always fixed, never estimated from the data.

Type:

float

decay

How coefficients shrink on longer lags.

Type:

Literal[‘harmonic’, ‘geometric’]

cross_shrinkage

Shrinkage on other variables’ lags vs own. 0 = only own lags, 1 = equal.

Type:

float

Expand for references to impulso.priors.MinnesotaPrior

The Minnesota Prior / Usage

The conjugate VAR: fast Bayesian estimation / When to reach for ConjugateVAR instead of the NUTS VAR / Scope

The Minnesota Prior, From Scratch

build_priors(n_vars, n_lags)

Build prior mean and standard deviation arrays for VAR coefficients.

Parameters:

• n_vars (int) – Number of endogenous variables.

• n_lags (int) – Number of lags.

Returns:

Dictionary with keys ‘B_mu’ and ‘B_sigma’ as numpy arrays.

Return type:

dict[str, ndarray]

model_config = {'frozen': True}

Configuration for the model, should be a dictionary conforming to [ConfigDict][pydantic.config.ConfigDict].