A New Monte Carlo Method for Computing Marginal Likelihoods

• Activity Number: 511
• Type: Invited
• Date/Time: Wednesday, August 12, 2015 : 10:30 AM to 12:20 PM
• Sponsor: Section on Statistical Computing
• Author(s): Yu-Bo Wang and Ming-Hui Chen and Lynn Kuo* and Paul O. Lewis
• Companies: University of Connecticut and University of Connecticut and University of Connecticut and University of Connecticut
• Keywords: Bayesian Model Selection ; Marginal Likelihood ; Inflated Density Estimator ; MCMC ; Harmonic Mean Estimator

Abstract

Evaluating the marginal likelihood in Bayesian analysis is essential in model selection. There are existing estimators based on a single MCMC sample from the posterior distribution, including the harmonic mean (HM) estimator proposed by Newton and Raftery (1994) and the inflated density ratio (IDR) estimator proposed by Petris and Tardella (2003). The HM estimator has been criticized for having large variance. The IDR estimator requires reparameterization and a careful selection of radius. We propose a new class of Monte Carlo estimators just based on this single MCMC sample. This class can be thought of as an HM estimator using an adaptively weighted kernel (likelihood times prior). We discuss how HM and IDR can be thought of as special cases of our proposed HAWK estimator. We also show that our estimator is consistent and has better theoretical properties than the HM and IDR estimators. In addition, we provide guidelines and an adaptive procedure on choosing the optimal weights. An extensive simulation study is conducted to examine the empirical performance of the proposed estimator and the methodology is applied to an analysis of the real data from a prostate cancer study.