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Variable selection over a potentially large set of covariates in a linearmodel is quite popular. In the Bayesian context, common prior choices can leadto a posterior expectation of the regression coefficients that is a sparse (ornearly sparse) vector with a few non-zero components, those covariates that aremost important. This article extends the global-local shrinkage idea to ascenario where one wishes to model multiple response variables simultaneously.Here, we have developed a variable selection method for a K-outcome model(multivariate regression) that identifies the most important covariates acrossall outcomes. The prior for all regression coefficients is a mean zero normalwith coefficient-specific variance term that consists of a predictor-specificfactor (shared local shrinkage parameter) and a model-specific factor (globalshrinkage term) that differs in each model. The performance of our modelingapproach is evaluated through simulation studies and a data example.

Bayesian Variable Selection for Multi-Outcome Models Through Shared Shrinkage