  We consider Bayesian logistic regression models with group-structured
covariates. In high-dimensional settings, it is often assumed that only small
portion of groups are significant, 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 performance of the proposed method outperforms existing
state-of-the-art methods in various settings. We further apply our method to an
MRI data set for predicting Parkinson's disease and show its benefits over
other contenders.
