On the selection consistency of Bayesian structured variable selection

A Bayesian variable selection framework is considered for analyzing image data. For the spatial dependencies to be modelled among the covariates, an Ising prior is assigned to the binary latent vector gamma, which indicates whether a covariate should be selected or not. The selection process, that is, the estimation of gamma, can be carried out with Gibbs sampler. Although the model has been used in many scientific applications, no theoretical development has been made. In this article, we established theories on the model selection consistency under mild conditions, which is an important theoretical property for high-dimensional variable selection. Copyright (C) 2017 John Wiley & Sons, Ltd.