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Bayesian group selection in logistic regression with application to MRI data analysis
Author(s) -
Lee Kyoungjae,
Cao Xuan
Publication year - 2021
Publication title -
biometrics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 2.298
H-Index - 130
eISSN - 1541-0420
pISSN - 0006-341X
DOI - 10.1111/biom.13290
Subject(s) - logistic regression , bayesian probability , frequentist inference , covariate , computer science , selection (genetic algorithm) , feature selection , statistics , consistency (knowledge bases) , bayesian linear regression , group selection , multinomial logistic regression , bayesian inference , data set , artificial intelligence , machine learning , mathematics
Abstract We consider Bayesian logistic regression models with group‐structured covariates. In high‐dimensional settings, it is often assumed that only a small portion of groups are significant, and thus, consistent group selection is of significant importance. While consistent frequentist group selection methods have been proposed, theoretical properties of Bayesian group selection methods for logistic regression models have not been investigated yet. In this paper, we consider a hierarchical group spike and slab prior for logistic regression models in high‐dimensional settings. Under mild conditions, we establish strong group selection consistency of the induced posterior, which is the first theoretical result in the Bayesian literature. Through simulation studies, we demonstrate that the proposed method outperforms existing state‐of‐the‐art methods in various settings. We further apply our method to a magnetic resonance imaging data set for predicting Parkinson's disease and show its benefits over other contenders.