A New Monte Carlo Method for Estimating Marginal Likelihoods.

TitleA New Monte Carlo Method for Estimating Marginal Likelihoods.
Publication TypeJournal Article
Year of Publication2018
AuthorsWang, Yu-Bo, Ming-Hui Chen, Lynn Kuo, and Paul O. Lewis
JournalBayesian Anal
Date Published2018 Jun

Evaluating the marginal likelihood in Bayesian analysis is essential for model selection. Estimators based on a single Markov chain Monte Carlo sample from the posterior distribution include the harmonic mean estimator and the inflated density ratio estimator. We propose a new class of Monte Carlo estimators based on this single Markov chain Monte Carlo sample. This class can be thought of as a generalization of the harmonic mean and inflated density ratio estimators using a partition weighted kernel (likelihood times prior). We show that our estimator is consistent and has better theoretical properties than the harmonic mean and inflated density ratio estimators. In addition, we provide guidelines on choosing optimal weights. Simulation studies were conducted to examine the empirical performance of the proposed estimator. We further demonstrate the desirable features of the proposed estimator with two real data sets: one is from a prostate cancer study using an ordinal probit regression model with latent variables; the other is for the power prior construction from two Eastern Cooperative Oncology Group phase III clinical trials using the cure rate survival model with similar objectives.

Alternate JournalBayesian Anal
Original PublicationA new Monte Carlo method for estimating marginal likelihoods.
PubMed ID29805725
PubMed Central IDPMC5967857
Grant ListP01 CA142538 / CA / NCI NIH HHS / United States
R01 GM070335 / GM / NIGMS NIH HHS / United States