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Model choice: A minimum posterior predictive loss approach. (English) Zbl 0904.62036

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.

MSC:

62F15 Bayesian inference
62J12 Generalized linear models (logistic models)
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