Using MCMC chain outputs to efficiently estimate Bayes factors

Richard D. Morey*, Jeffrey N. Rouder, Michael S. Pratte, Paul L. Speckman

*Corresponding author for this work

Research output: Contribution to journalArticleAcademicpeer-review

42 Citations (Scopus)

Abstract

One of the most important methodological problems in psychological research is assessing the reasonableness of null models, which typically constrain a parameter to a specific value such as zero. Bayes factor has been recently advocated in the statistical and psychological literature as a principled means of measuring the evidence in data for various models, including those where parameters are set to specific values. Yet, it is rarely adopted in substantive research, perhaps because of the difficulties in computation. Fortunately, for this problem, the Savage-Dickey density ratio (Dickey & Lientz, 1970) provides a conceptually simple approach to computing Bayes factor. Here, we review methods for computing the Savage-Dickey density ratio, and highlight an improved method, originally suggested by Gelfand and Smith (1990) and advocated by Chib (1995), that outperforms those currently discussed in the psychological literature. The improved method is based on conditional quantities, which may be integrated by Markov chain Monte Carlo sampling to estimate Bayes factors. These conditional quantities efficiently utilize all the information in the MCMC chains, leading to accurate estimation of Bayes factors. We demonstrate the method by computing Bayes factors in one-sample and one-way designs, and show how it may be implemented in WinBUGS. (C) 2011 Elsevier Inc. All rights reserved.

Original languageEnglish
Pages (from-to)368-378
Number of pages11
JournalJournal of Mathematical Psychology
Volume55
Issue number5
DOIs
Publication statusPublished - Oct-2011

Keywords

  • Bayesian statistics
  • Bayesian inference
  • Bayes factors
  • Markov chain Monte Carlo
  • ANOVA
  • Encompassing priors
  • POSTERIOR DENSITY-ESTIMATION
  • WEIGHTED LIKELIHOOD RATIO
  • NULL HYPOTHESIS
  • P-VALUES
  • SELECTION
  • PRIORS

Cite this