Publications [#258249] of Alan E. Gelfand
search .Papers Published
- Gelfand, AE; Ghosh, SK. "Model choice: A minimum posterior predictive loss approach." Biometrika 85.1 (January, 1998): 1-11. [doi]
(last updated on 2023/06/01)Abstract:
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 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.