Posterior Consistency for Bayesian Relevance Vector Machines
Xiao Fang, Malay Ghosh; 24(174):1−17, 2023.
Abstract
The problem of statistical modeling and inference with sample sizes substantially smaller than the number of available covariates poses challenges. In a previous study, Chakraborty et al. (2012) conducted a hierarchical Bayesian analysis of nonlinear regression in such situations using relevance vector machines based on reproducing kernel Hilbert space (RKHS). However, they did not provide any theoretical properties associated with their procedure. This paper addresses the same problem, introduces a new class of global-local priors different from the previous study, and presents results on posterior consistency as well as on posterior contraction rates.
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