Bayesian model selection using encompassing priors

Irene Klugkist, Bernet Kato and Herbert Hoijtink

Statistica Neerlandica, 2005, vol. 59, issue 1, 57-69

Abstract: This paper deals with Bayesian selection of models that can be specified using inequality constraints among the model parameters. The concept of encompassing priors is introduced, that is, a prior distribution for an unconstrained model from which the prior distributions of the constrained models can be derived. It is shown that the Bayes factor for the encompassing and a constrained model has a very nice interpretation: it is the ratio of the proportion of the prior and posterior distribution of the encompassing model in agreement with the constrained model. It is also shown that, for a specific class of models, selection based on encompassing priors will render a virtually objective selection procedure. The paper concludes with three illustrative examples: an analysis of variance with ordered means; a contingency table analysis with ordered odds‐ratios; and a multilevel model with ordered slopes.

Date: 2005
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