2022/03/14 by Xuan Cao, Cao, Xuan, Kyoungjae Lee +1
Computer Science · Mathematics · #Bayesian Methods and Mixture Models #FOS: Computer and information sciences #FOS: Mathematics #Methodology (stat.ME) #Statistical Methods and Bayesian Inference #Statistical Methods and Inference #Statistics Theory (math.ST)
paper · pdf · doi:10.48550/arxiv.2203.07110
openalex publication_date 2022/03/14 · openalex created_date 2023/03/01 · openalex updated_date 2026/07/28
Variable selection methods with nonlocal priors have been widely studied in\nlinear regression models, and their theoretical and empirical performances have\nbeen reported. However, the crucial model selection properties for hierarchical\nnonlocal priors in high-dimensional generalized linear regression have rarely\nbeen investigated. In this paper, we consider a hierarchical nonlocal prior for\nhigh-dimensional logistic regression models and investigate theoretical\nproperties of the posterior distribution. Specifically, a product moment (pMOM)\nnonlocal prior is imposed over the regression coefficients with an\nInverse-Gamma prior on the tuning parameter. Under standard regularity\nassumptions, we establish strong model selection consistency in a\nhigh-dimensional setting, where the number of covariates is allowed to increase\nat a sub-exponential rate with the sample size. We implement the Laplace\napproximation for computing the posterior probabilities, and a modified shotgun\nstochastic search procedure is suggested for efficiently exploring the model\nspace. We demonstrate the validity of the proposed method through simulation\nstudies and an RNA-sequencing dataset for stratifying disease risk.\n