Bayesian Estimation and Variable Selection in Multivariate Generalized Linear Models

• Activity Number: 74 - Invited E-Poster Session I
• Type: Invited
• Date/Time: Sunday, August 7, 2022 : 8:30 PM to 9:25 PM
• Sponsor: International Society for Bayesian Analysis (ISBA)
• Author(s): Ray Bai* and Hsin-Hsiung Huang and Shao-Hsuan Wang
• Companies: University of South Carolina and University of Central Florida and National Central University
• Keywords: posterior contraction; generalized linear model; latent Gaussian model; multivariate regression; non-Gaussian data

Abstract

In this presentation, we consider Bayesian estimation and variable selection in generalized linear models (GLMs) with multivariate, correlated responses that could be both discrete (e.g. binary and count) and continuous. Our approach, which we call the Multivariate Bayesian model with Shrinkage Priors for GLMs (MBSP-GLM), simultaneously models the multiple (possibly mixed-type) response variables by employing a latent Gaussian distribution to induce correlations between the responses. Meanwhile, global-local shrinkage priors are used to obtain a (nearly) sparse estimate of the regression coefficients matrix. We derive the posterior contraction rate for MBSP-GLM when the number of covariates grows subexponentially and the number of responses grows sublinearly with sample size. To the best of our knowledge, this is the first posterior contraction result for multivariate Bayesian GLMs. We illustrate our method on a clinical application with multiple binary and count responses.