A Comparison of Monte Carlo Based Marginal Likelihood Estimators

Marginal likelihood plays a central role in Bayesian model comparison and hypothesis testing, but its computation is often challenging in practice. This article reviews recent Monte Carlo methods that rely on the availability of Markov chain Monte Carlo (MCMC) samples from the posterior and prior distributions along with the corresponding unnormalized kernels that can be evaluated numerically. Within this scope, we summarize the strengths, limitations, differences, and connections of different methods. Two in‐depth applications are presented to illustrate their relative performance. This article is categorized under: Statistical and Graphical Methods of Data Analysis > Monte Carlo Methods Statistical Models > Model Selection Statistical Models > Bayesian Models