An analytical study of several markov chain monte carlo estimators of the marginal likelihood

Joan Z. Yu*, Martin A. Tanner

*Corresponding author for this work

Research output: Contribution to journalArticle

4 Scopus citations

Abstract

An approach to calculating the marginal likelihood (ML) by the Gibbs stopper is examined. The moments of the estimator are investigated assuming a normal posterior distribution. The analytical expectation and variance for a variety of ML estimators based on the Gibbs stopper, as well as based on another approach proposed by Chib, are derived and are compared. It is found that even in relatively simple situations (e.g., bivariate and multivariate normal posteriors), an estimator can have infinite variance, especially when the parameters are highly correlated. Some fixes to this phenomena are proposed and asymptotic properties of the estimators are discussed. The estimators are applied to real data.

Original languageEnglish (US)
Pages (from-to)839-853
Number of pages15
JournalJournal of Computational and Graphical Statistics
Volume8
Issue number4
DOIs
StatePublished - Dec 1999

Keywords

  • Bayes factor
  • Gibbs sampler
  • Gibbs stopper
  • Importance sampling
  • Mixture model

ASJC Scopus subject areas

  • Statistics and Probability
  • Discrete Mathematics and Combinatorics
  • Statistics, Probability and Uncertainty

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