Abstract

The task of calculating marginal likelihoods arises in a wide array of statistical inference problems, including the evaluation of Bayes factors for model selection and hypothesis testing. Although Markov chain Monte Carlo methods have simplified many posterior calculations needed for practical Bayesian analysis, the evaluation of marginal likelihoods remains difficult. We consider the behavior of the wellknown harmonic mean estimator (Newton and Raftery, 1994) of the marginal likelihood, which converges almost-surely but may have infinite variance and so may not obey a central limit theorem.

Citations