On Bayesian calculations for mixture likelihoods and priors.
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.
Weiss
R E
RE
Department of Biostatistics, UCLA School of Public Health, Los Angeles, CA 90095-1772, USA. rob@rem.ph.ucla.edu
Cho
M
M
Yanuzzi
M
M
D001499:Bayes Theorem; D002648:Child; D005260:Female; D006801:Humans; D007230:Infant, Low Birth Weight / Q000502:physiology; D007231:Infant, Newborn; D016013:Likelihood Functions; D016015:Logistic Models; D008297:Male; D008390:Markov Chains; D008954:Models, Biological; D009010:Monte Carlo Method; D009716:Numerical Analysis, Computer-Assisted; D010147:Pain Measurement / Q000523:psychology; D011897:Random Allocation; D013636:Tanzania