© 1998 by Biometrika Trust
Model choice: A minimum posterior predictive loss approach
Department of Statistics, University of Connecticut Storrs, Connecticut 06269-3120, U.S.A. alan{at}stat.uconn.edu
Department of Statistics, North Carolina State University Raleigh, North Carolina, 27695-8203, U.S.A. sghosh{at}stat.ncsu.edu
Model choice is a fundamental and much discussed activity in the analysis of datasets. Nonnested 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 minirnises 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.
Key Words: Censored data • Deviance • Exponential family • Generalised linear model • Penalty function • Utility function
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