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.
Funding Statement
This work was supported in part by the Simons Foundation’s collaboration grant (No.635213) and the Taft Summer Research Fellowship at University of Cincinnati. This paper was supported by Samsung Research Fund, Sungkyunkwan University, 2022.
Acknowledgments
We are grateful to the Associate Editor and reviewer for their valuable comments which have significantly improved the quality of presentation and technical content of our paper.
Citation
Xuan Cao. Kyoungjae Lee. "Bayesian Inference on Hierarchical Nonlocal Priors in Generalized Linear Models." Bayesian Anal. 19 (1) 99 - 122, March 2024. https://doi.org/10.1214/22-BA1350
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