Posterior Consistency for Bayesian Relevance Vector Machines
This provides theoretical validation for a Bayesian method in high-dimensional settings, which is incremental but important for statistical rigor.
The paper addresses the lack of theoretical guarantees for Bayesian relevance vector machines in high-dimensional regression by introducing a new class of global-local priors and proving posterior consistency and contraction rates.
Statistical modeling and inference problems with sample sizes substantially smaller than the number of available covariates are challenging. Chakraborty et al. (2012) did a full hierarchical Bayesian analysis of nonlinear regression in such situations using relevance vector machines based on reproducing kernel Hilbert space (RKHS). But they did not provide any theoretical properties associated with their procedure. The present paper revisits their problem, introduces a new class of global-local priors different from theirs, and provides results on posterior consistency as well as posterior contraction rates