feat: variable selection priors for SSTS covariates - #1112
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## issue-758-ssts-covariates #1112 +/- ##
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Wire VariableSelectionPrior (spike-and-slab, horseshoe, normal) to the StateSpaceTimeSeries regression coefficients via vs_prior_type and vs_hyperparams, mirroring InstrumentalVariableRegression. The generic prior loop special-cases beta_exog when configured. Expose get_inclusion_probabilities() and get_shrinkage_factors() pass-throughs (groundwork for the inclusion plot in #758 P6). Prototype-verified: sampling is clean and inclusion probabilities rank true predictors first. beta_exog point estimates attenuate toward zero because P0 lets the regression states drift from the parameter; pinning the exog P0 entries fixes that on paper but makes NUTS pathologically slow, so the caveat is documented instead. Counterfactual forecasts use the smoothed states and are unaffected.
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Closes #981. Part of #758 (P0). Stacked on #1111, review that one first. Targets
pymc6_and_pymcmarketing1_migration.Adds
vs_prior_type("spike_and_slab", "horseshoe", or "normal", the same set the factory accepts) andvs_hyperparamstoStateSpaceTimeSeries, mirroringInstrumentalVariableRegressionand reusingcausalpy/variable_selection_priors.pyunchanged. When set, thebeta_exogprior is built by the factory instead of the default. Passing bothpriors={"beta_exog": ...}andvs_prior_typelets variable selection win, with a warning, same as the IV class. Setting it without covariates raises at build time.get_inclusion_probabilities()andget_shrinkage_factors()are thin pass-throughs to the factory, which prepares the P6 plotting item of #758.Known caveat, documented and accepted:
beta_exogpoint estimates shrink toward zero, becauseP0(the initial state covariance, unrelated to the P0 priority label of #758) lets the regression states drift away from the parameter. Pinning the exogP0entries fixes the statistics on paper but makes NUTS pathologically slow, 15+ minutes against about 2, so it is not done here. Counterfactual forecasts ride on the smoothed states, which do recover the truth, and selection uses the inclusion-probability ranking, which is correct.Tests assert API shape, dims and coords only. The suite mocks
pm.sample, so posterior recovery cannot be asserted there. Selection behavior was checked in a prototype and is demonstrated in the notebook in the next PR.Verified locally with pymc 6.2.0, arviz 1.2.0, pymc-extras 0.14.0: 1407 passed, 17 skipped.