Bayesian inference on hierarchical nonlocal priors in generalized linear models

TL;DR

This paper develops a Bayesian hierarchical nonlocal prior approach for high-dimensional logistic regression, establishing strong model selection consistency and demonstrating its effectiveness through simulations and real data analysis.

Contribution

It introduces a hierarchical nonlocal prior framework for high-dimensional logistic regression and proves its strong model selection consistency under regularity conditions.

Findings

Achieves strong model selection consistency in high-dimensional settings.

Effective posterior computation via Laplace approximation and stochastic search.

Validated through simulations and RNA-sequencing data analysis.

Abstract

Variable selection methods with nonlocal priors have been widely studied in linear regression models, and their theoretical and empirical performances have been reported. However, the crucial model selection properties for hierarchical nonlocal priors in high-dimensional generalized linear regression have rarely been investigated. In this paper, we consider a hierarchical nonlocal prior for high-dimensional logistic regression models and investigate theoretical properties of the posterior distribution. Specifically, a product moment (pMOM) nonlocal prior is imposed over the regression coefficients with an Inverse-Gamma prior on the tuning parameter. Under standard regularity assumptions, we establish strong model selection consistency in a high-dimensional setting, where the number of covariates is allowed to increase at a sub-exponential rate with the sample size. We implement the Laplace approximation for computing the posterior probabilities, and a modified shotgun stochastic search procedure is suggested for efficiently exploring the model space. We demonstrate the validity of the proposed method through simulation studies and an RNA-sequencing dataset for stratifying disease risk.