Work

Two-step mixed-type multivariate Bayesian sparse variable selection with shrinkage priors

Year: 2025

Type: article

Abstract: We introduce a Bayesian framework for mixed-type multivariate regression using continuous shrinkage priors. Our framework enables joint analysis of mixed continuous and discrete outcomes and facilitates variable selection from the p covariates. Theoretical studies of Bayesian mixed-type multivariate response models have not been conducted previously and require more intricate arguments than the corresponding theory for univariate response models due to the correlations between the responses. In this paper, we investigate necessary and sufficient conditions for posterior contraction of our method when p grows faster than sample size n. The existing literature on Bayesian high-dimensional asymptotics has focused only on cases where p grows subexponentially with n. In contrast, we study the asymptotic regime where p is allowed to grow exponentially in terms of n. We develop a novel two-step approach for variable selection which possesses the sure screening property and provably achieves posterior contraction even under exponential growth of p. We demonstrate the utility of our method through simulation studies and applications to real data, including a cancer genomics dataset where n=174 and p=9183. The R code to implement our method is available at https://github.com/raybai07/MtMBSP.

Source: Electronic Journal of Statistics

DOI: 10.1214/25-ejs2343

Authors: Shao-Hsuan Wang, Ray Bai, Hsin-Hsiung Huang

Institutions: National Central University, University of South Carolina, University of Central Florida

Language: English

Topic: Statistical Methods and Inference

Subfield: Statistics and Probability

Field: Mathematics

Domain: Physical Sciences

Open Access status: gold

Estimated APC paid: $675

Funder: National Science Foundation