`bayesian_ridge` – Bayesian ridge with empirical-Bayes prior.#

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Operational op under axis family, sub-layer L4_A_model_selection, layer l4. Standalone callable: mf.functions.bayesian_ridge_fit.

Function signature#

mf.functions.bayesian_ridge_fit(
    X: np.ndarray | pd.DataFrame,
    y: np.ndarray | pd.Series,
) -> BayesianRidgeFitResult

Parameters#

name	type	default	constraint	description
`X`	`np.ndarray	pd.DataFrame`	—	—
`y`	`np.ndarray	pd.Series`	—	—

Returns#

BayesianRidgeFitResult — frozen dataclass with fit results.

Attribute	Type	Description
`.coef_`	`np.ndarray`	Posterior mean coefficient vector, shape (n_features,).
`.intercept_`	`float`	Posterior mean intercept scalar.
`.alpha_`	`float`	Posterior noise precision (empirical Bayes).
`.lambda_`	`float`	Posterior weight precision (empirical Bayes).
`.predict(X)`	`np.ndarray`	Predictions for new data X, shape (n_samples,).
`.summary()`	`str`	Human-readable text table of fit results.

Behavior#

sklearn BayesianRidge: gamma priors on noise + coefficient precision; type-II ML estimates of both. Returns posterior mean coefficients + posterior variance. Useful when the user wants a coefficient credible interval without bootstrapping.

When to use

Studies that need coefficient credible intervals; default-Bayesian baselines.

In recipe context#

Set params.family = "bayesian_ridge" in the relevant layer to activate this op within a recipe:

# Layer L4 recipe fragment
params:
  family: bayesian_ridge

References#

macroforecast design Part 2, L4: ‘forecasting model is the layer where every authoring iteration ends – pick family, tune, repeat.’

bayesian_ridge – Bayesian ridge with empirical-Bayes prior.#