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As more data being collected nowadays, it is common to analyze multiplerelated responses from the same study. Existing variable selection methodsselect variables for all responses without considering that some features mayonly predict a subset of responses but not the rest. Motivated by themulti-trait fine mapping problem in genetics, we develop a novel Bayesianindicator variable selection method with a large number of grouped predictorstargeting at multiple correlated and possibly heterogeneous responses. Weshowed the advantage of our method via extensive simulations and a fine mappingexample to identify causal variants associated with multiple addictivebehaviors.

Bayesian indicator variable selection of multivariate response with heterogeneous sparsity for multi-trait fine mapping