Fully and empirical Bayes approaches to estimating copula-based models for bivariate mixed outcomes using Hamiltonian Monte Carlo

Abstract

We provide a fully Bayesian approach to conduct estimation and inference for a copula model to jointly analyze bivariate mixed outcomes. To obtain posterior samples, we use Hamiltonian Monte Carlo, which avoids the random walk behavior of Metropolis and Gibbs sampling algorithms. We also provide an empirical Bayes approach to estimate the copula parameter, which is useful when prior specification on that parameter is difficult. We further propose the use of Bayesian model selection criteria to select the most appropriate copula family. We conduct simulation studies to compare the two approaches and to examine copula selection performance and illustrate the application of the fully Bayesian approach on a burn injury data set.