Bayesian Model Choice Via Markov Chain Monte Carlo Methods

TLDR

Markov chain Monte Carlo integration methods have enabled fitting highly complex Bayesian models, yet model comparison is hampered by convergence violations. This work introduces a Bayesian model‑choice framework and an MCMC algorithm that overcomes these convergence problems. The algorithm handles single‑model scenarios with unknown dimensionality, such as integer parameters, changepoints, or finite mixtures, and is demonstrated on two published examples.

Abstract

SUMMARY Markov chain Monte Carlo (MCMC) integration methods enable the fitting of models of virtually unlimited complexity, and as such have revolutionized the practice of Bayesian data analysis. However, comparison across models may not proceed in a completely analogous fashion, owing to 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 convergence difficulties. Our algorithm applies equally well to problems where only one model is contemplated but its proper size is not known at the outset, such as problems involving integer-valued parameters, multiple changepoints or finite mixture distributions. We illustrate our approach with two published examples.