Bayesian Analysis

A New Monte Carlo Method for Estimating Marginal Likelihoods

Yu-Bo Wang, Ming-Hui Chen, Lynn Kuo, and Paul O. Lewis

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Abstract

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.

Article information

Source
Bayesian Anal. (2017), 23 pages.

Dates
First available in Project Euclid: 28 February 2017

Permanent link to this document
https://projecteuclid.org/euclid.ba/1488250818

Digital Object Identifier
doi:10.1214/17-BA1049

Keywords
Bayesian model selection cure rate model harmonic mean estimator inflated density ratio estimator ordinal probit regression power prior

Rights
Creative Commons Attribution 4.0 International License.

Citation

Wang, Yu-Bo; Chen, Ming-Hui; Kuo, Lynn; Lewis, Paul O. A New Monte Carlo Method for Estimating Marginal Likelihoods. Bayesian Anal., advance publication, 28 February 2017. doi:10.1214/17-BA1049. https://projecteuclid.org/euclid.ba/1488250818


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