Bayesian group selection with non-local priors

In many applications, variables or features can be naturally partitioned into different groups. In this article, we propose a new Bayesian hierarchical model for group selection problem when the group structure is known. We use spike and slab priors for regression coefficients, and the slab component is assumed to come from the family of nonlocal priors. Contrary to local priors commonly used in Bayesian group selection, nonlocal density priors vanish when a regression coefficient in the model is zero. We use simulation studies to assess the performance of our method and apply it to data collected from individuals undergoing cardiac catheterization at Duke University Medical center between 2001 and 2010.