BAYESIAN MODEL CHOICE VIA MARKOV-CHAIN MONTE-CARLO METHODS

Markov chain Monte Carlo (MCMC) integration methods enable the fitting of models of virtually unlimited complexity, and as such have revolut ionized the practice of Bayesian data analysis. However, comparison ac ross models may not proceed in a completely analogous fashion, owing t o violations of the conditions sufficient to ensure convergence of the Markov chain. In this paper we present a framework for Bayesian model choice, along with an MCMC algorithm that does not suffer from conver gence difficulties. Our algorithm applies equally well to problems whe re only one model is contemplated but its proper size is not known at the outset, such as problems involving integer-valued parameters, mult iple changepoints or finite mixture distributions. We illustrate our a pproach with two published examples.