A0211
Title: Mixed-type multivariate Bayesian sparse variable selection with shrinkage priors
Authors: Shao-Hsuan Wang - National Central University (Taiwan) [presenting]
Hsin-Hsiung Huang - University of Central Florida (United States)
Ray Bai - University of South Carolina (United States)
Abstract: A Bayesian framework is introduced for mixed-type multivariate regression using shrinkage priors. The proposed method enables joint analysis of mixed continuous and discrete outcomes and facilitates variable selection when the number of covariates p can be much larger than sample size $n$. Theoretically, we show that the posterior contracts around the true parameter in mixed-response models when $p$ grows subexponentially with $n$. To cope with the high computational cost when $p$ is large, we introduce a simple two-step variable selection approach. We prove that our two-step algorithm possesses the sure screening property and achieves a faster mixing time than the conventional one-step Gibbs sampler. Moreover, our two-step estimator can provably achieve posterior consistency even when $p$ grows exponentially in $n$, thus overcoming a limitation of the one-step estimator. Numerical studies and analyses of real datasets demonstrate the ability of our joint modeling approach to improve predictive accuracy and identify significant variables in multivariate mixed response models.
