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Bayesian model selection using encompassing priors
Author(s) -
Klugkist Irene,
Kato Bernet,
Hoijtink Herbert
Publication year - 2005
Publication title -
statistica neerlandica
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.52
H-Index - 39
eISSN - 1467-9574
pISSN - 0039-0402
DOI - 10.1111/j.1467-9574.2005.00279.x
Subject(s) - prior probability , bayes factor , model selection , mathematics , contingency table , selection (genetic algorithm) , bayesian probability , bayesian inference , variance (accounting) , bayesian hierarchical modeling , posterior probability , categorical distribution , econometrics , computer science , statistics , artificial intelligence , accounting , business
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.