文章基本信息

标题：A New Monte Carlo Method for Estimating Marginal Likelihoods
本地全文：下载
作者：Yu-Bo Wang ; Ming-Hui Chen ; Lynn Kuo 等
期刊名称：Bayesian Analysis
印刷版ISSN：1931-6690
电子版ISSN：1936-0975
出版年度：2018
卷号：13
期号：2
页码：311-333
DOI：10.1214/17-BA1049
语种：English
出版社：International Society for Bayesian Analysis
摘要：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 in- flated 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.
关键词：Bayesian model selection; cure rate model; harmonic mean estimator;inflated density ratio estimator; ordinal probit regression; power prior.