Variable selection and shrinkage (SSVS)

Why shrinkage?

Bayesian VARs can include many coefficients (lags \times variables \times equations). Shrinkage priors regularise the model and can improve forecast performance.

SSVS intuition

Stochastic search variable selection (SSVS) places a mixture prior on coefficients so that, conditional on an inclusion indicator, a coefficient is either:

  • heavily shrunk towards zero (“spike”), or

  • allowed to vary more freely (“slab”).

In this toolkit

The Python toolkit supports an SSVS-style prior for reduced-form VAR coefficients:

  • a latent boolean vector gamma controls which coefficient rows are in the spike or slab regime,

  • Gibbs updates alternate between sampling VAR parameters and updating gamma.

This implementation is designed for practical forecasting workflows rather than reproducing every shrinkage variant in the paper.

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