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On Bayesian calculations for mixture likelihoods and priors
Author(s) -
Weiss Robert E.,
Cho Meehyung,
Yanuzzi Michael
Publication year - 1999
Publication title -
statistics in medicine
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.996
H-Index - 183
eISSN - 1097-0258
pISSN - 0277-6715
DOI - 10.1002/(sici)1097-0258(19990630)18:12<1555::aid-sim145>3.0.co;2-x
Subject(s) - markov chain monte carlo , prior probability , computer science , bayesian probability , model selection , bayes' theorem , bayes factor , posterior probability , approximate bayesian computation , statistics , logistic regression , mathematics , artificial intelligence , machine learning , inference
We present methodology for calculating Bayes factors between models as well as posterior probabilities of the models when the indicator variables of the models are integrated out of the posterior before Markov chain Monte Carlo (MCMC) computations. Standard methodology would include the indicator functions as part of the MCMC computations. We demonstrate that our methodology can give substantially greater accuracy than the traditional approach. We illustrate the methodology using the model selection prior of George and McCulloch applied to logistic regression and to a mixture model for observations in a hierarchical random effects model. Copyright © 1999 John Wiley & Sons, Ltd.