Bayesian variable selection for non-Gaussian responses: a marginally calibrated copula approach

Abstract

We propose a new highly flexible and tractable Bayesian approach to undertake variable selection in non-Gaussian regression models. It uses a copula decomposition for the joint distribution of observations on the dependent variable. This allows the marginal distribution of the dependent variable to be calibrated accurately using a nonparametric or other estimator. The family of copulas employed are "implicit copulas" that are constructed from existing hierarchical Bayesian models widely used for variable selection, and we establish some of their properties. Even though the copulas are high dimensional, they can be estimated efficiently and quickly using Markov chain Monte Carlo. A simulation..