Bayesian model choice based on Monte Carlo estimates of posterior model probabilities

Arange of approximatemethods have been proposed formodel choice based onBayesian principles, given the problems involved in multiple integration in multi-parameter problems. Formal Bayesian model assessment is based on prior model probabilities P(M = j) and posterior model probabilities P(M = j |Y ) after observing the data. An approach is outlined here that produces posterior model probabilities and hence Bayes factor estimates but not marginal likelihoods. It uses a Monte Carlo approximation based on independentMCMCsampling of two ormore differentmodels.While parallel sampling of the models is not necessary, such a form of sampling facilitates model averaging and assessing the impact of individual observations on the overall estimated Bayes factor. Three worked examples used before in model choice studies illustrate application of the method. © 2004 Elsevier B.V. All rights reserved.