Computational Statistics & Data Analysis 48 (2005) 735–753 www.elsevier.com/locate/csda Bayesian predictive model comparison via parallel sampling P. Congdon ∗ Department of Geography, Queen Mary University of London, Mile End Rd, London E1 4NS, UK Received 18 March 2004; accepted 18 March 2004 Abstract Methods of model comparison and checking, and associated criteria, are proposed based on parallel sampling of two or more models subsequent to convergence. These complement Bayesian predictive criteria already proposed (e.g. error sum of squares and deviance based) but are on a scale that may be compared across applications. Penalised criteria for model comparison based on the AIC are also investigated, together with AIC model weights and evidence ratios. Parallel sampling enables posterior summaries to be obtained for continuous comparison measures (e.g. likelihood and evidence ratios). A forward selection procedure for regression is suggested as one possible extension, as well as procedures for model averaging and posterior predictive checking. Comparisons with the DIC are made together with implications of parallel sampling for assessing the density of the DIC. Three worked examples illustrate the working of the procedures in practice. c  2004 Elsevier B.V. All rights reserved. Keywords: Predictive model comparison; Model checking; Parallel sampling; Predictor selection; Penalties for complexity 1. Introduction Formal Bayesian model choice is based on marginal likelihoods of dierent models and resulting Bayes factors. However, the methodology of Bayes factors is complicated by computational complexities in obtaining marginal likelihoods (Han and Carlin, 2001; Ntzoufras et al., 2004) and by the sensitivity of the Bayes factor. The Bayes factor B 21 when model 2 is more complex than model 1 tends to zero as sample size n increases, * Tel.: +0207-882-7760; fax: +0208-981-6276. E-mail address: p.congdon@qmul.ac.uk (P. Congdon). 0167-9473/$ - see front matter c  2004 Elsevier B.V. All rights reserved. doi:10.1016/j.csda.2004.03.016