Asymptotic Theory of Bayes Factor for Nonparametric Model and Variable Selection in the Gaussian Process Framework.

In this paper we consider the Bayes factor approach to general model and variable selection under a nonparametric, Gaussian process framework. Specifically, we establish that under reasonable conditions, the Bayes factor consistently selects the correct model with exponentially fast convergence rate. If the true model does not belong to the postulated model space, then the Bayes factor asymptotically selects the best possible model in the model space with exponentially fast convergence rate. We derive several theoretical applications of the proposed method to various setups like the simple linear regression, reproducing kernel Hilbert space (RKHS) models, autoregressive (AR) models, and combinations of such models.