Gelfand, Alan E.; Ghosh, Sujit K. Model choice: A minimum posterior predictive loss approach. (English) Zbl 0904.62036 Biometrika 85, No. 1, 1-11 (1998). Summary: Model choice is a fundamental and much discussed activity in the analysis of data sets. Non-nested hierarchical models introducing random effects may not be handled by classical methods. Bayesian approaches using predictive distributions can be used though the formal solution, which includes Bayes factors as a special case, can be criticised. We propose a predictive criterion where the goal is good prediction of a replicate of the observed data but tempered by fidelity to the observed values. We obtain this criterion by minimising posterior loss for a given model and then, for models under consideration, selecting the one which minimises this criterion. For a broad range of losses, the criterion emerges as a form partitioned into a goodness-of-fit term and a penalty term. We illustrate its performance with an application to a large dataset involving residential property transactions. Cited in 3 ReviewsCited in 132 Documents MSC: 62F15 Bayesian inference 62J12 Generalized linear models (logistic models) Keywords:censored data; deviance; exponential family; penalty function; utility function PDFBibTeX XMLCite \textit{A. E. Gelfand} and \textit{S. K. Ghosh}, Biometrika 85, No. 1, 1--11 (1998; Zbl 0904.62036) Full Text: DOI Link