Bayesian group selection in logistic regression with application to MRI data analysis

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.