Partition Weighted Approach for Estimating the Marginal Posterior Density with Applications.

TitlePartition Weighted Approach for Estimating the Marginal Posterior Density with Applications.
Publication TypeJournal Article
Year of Publication2019
AuthorsWang, Yu-Bo, Ming-Hui Chen, Lynn Kuo, and Paul O. Lewis
JournalJ Comput Graph Stat
Date Published2019

The computation of marginal posterior density in Bayesian analysis is essential in that it can provide complete information about parameters of interest. Furthermore, the marginal posterior density can be used for computing Bayes factors, posterior model probabilities, and diagnostic measures. The conditional marginal density estimator (CMDE) is theoretically the best for marginal density estimation but requires the closed-form expression of the conditional posterior density, which is often not available in many applications. We develop the partition weighted marginal density estimator (PWMDE) to realize the CMDE. This unbiased estimator requires only a single MCMC output from the joint posterior distribution and the known unnormalized posterior density. The theoretical properties and various applications of the We carry out simulation studies to investigate the empirical performance of the PWMDE and further demonstrate the desirable features of the proposed method with two real data sets from a study of dissociative identity disorder patients and a prostate cancer study, respectively.

Alternate JournalJ Comput Graph Stat
Original PublicationPartition weighted approach for estimating the marginal posterior density with applications.
PubMed ID31263347
PubMed Central IDPMC6602590
Grant ListP01 CA142538 / CA / NCI NIH HHS / United States
R01 GM070335 / GM / NIGMS NIH HHS / United States