An Approach of Bayesian Variable Selection for Ultrahigh Dimensional Multivariate Regression

TL;DR

This paper introduces a Bayesian multivariate variable selection method tailored for ultrahigh-dimensional data, effectively identifying predictors associated with multiple correlated responses while accounting for their covariance structure.

Contribution

It proposes a novel Bayesian approach with sample-size-dependent priors that achieves strong selection consistency and outperforms existing methods in high-dimensional multivariate regression.

Findings

Outperforms existing Bayesian and frequentist methods in simulations.

Effectively models covariance among multiple responses without assuming independence.

Demonstrates applicability to genome-wide association studies with real data.

Abstract

In many practices, scientists are particularly interested in detecting which of the predictors are truly associated with a multivariate response. It is more accurate to model multiple responses as one vector rather than separating each component one by one. This is particularly true for complex traits having multiple correlated components. A Bayesian multivariate variable selection (BMVS) approach is proposed to select important predictors influencing the multivariate response from a candidate pool with an ultrahigh dimension. By applying the sample-size-dependent spike and slab priors, the BMVS approach satisfies the strong selection consistency property under certain conditions, which represents the advantages of BMVS over other existing Bayesian multivariate regression-based approaches. The proposed approach considers the covariance structure of multiple responses without assuming independence and integrates the estimation of covariance-related parameters together with all regression parameters into one framework through a fast updating MCMC procedure. It is demonstrated through simulations that the BMVS approach outperforms some other relevant frequentist and Bayesian approaches. The proposed BMVS approach possesses the flexibility of wide applications, including genome-wide association studies with multiple correlated phenotypes and a large scale of genetic variants and/or environmental variables, as demonstrated in the real data analyses section. The computer code and test data of the proposed method are available as an R package.