Consistent group selection using nonlocal priors in regression

In many applications, variables can be naturally partitioned into different groups. We consider a hierarchical model with nonlocal priors over group-structured covariates to perform group selection in high-dimensional linear regression. While several frequentist and Bayesian approaches have been proposed for group selection, theoretical properties of Bayesian approaches using nonlocal priors have not been studied. Under mild conditions, we establish strong group selection consistency of the induced posterior when the number of covariates grows at nearly exponential rate with sample size. An efficient shotgun stochastic search algorithm tailored for the group selection is adopted for implementing our proposed approach and simulation studies are conducted to demonstrate its superior empirical performance. We further apply the proposed method to an fMRI dataset for identifying brain regions with altered functional activities to predict disease progression.