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

Travis CanidaHongjie KeTianzhou Ma
Dec 2022
Variable selection has been played a critical role in contemporary statisticsand scientific discoveries. Numerous regularization and Bayesian variableselection methods have been developed in the past two decades for variableselection, but they mainly target at only one response. As more data beingcollected nowadays, it is common to obtain and analyze multiple correlatedresponses from the same study. Running separate regression for each responseignores their correlation thus multivariate analysis is recommended. Existingmultivariate methods select variables related to all responses withoutconsidering the possible heterogeneous sparsity of different responses, i.e.some features may only predict a subset of responses but not the rest. In thispaper, we develop a novel Bayesian indicator variable selection method inmultivariate regression model with a large number of grouped predictorstargeting at multiple correlated responses with possibly heterogeneous sparsitypatterns. The method is motivated by the multi-trait fine mapping problem ingenetics to identify the variants that are causal to multiple related traits.Our new method is featured by its selection at individual level, group level aswell as specific to each response. In addition, we propose a new concept ofsubset posterior inclusion probability for inference to prioritize predictorsthat target at subset(s) of responses. Extensive simulations with varyingsparsity and heterogeneity levels and dimension have shown the advantage of ourmethod in variable selection and prediction performance as compared to existinggeneral Bayesian multivariate variable selection methods and Bayesian finemapping methods. We also applied our method to a real data example in imaginggenetics and identified important causal variants for brain white matterstructural change in different regions.