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Abstract:
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It is widely accepted that the Bayes factor is a key tool in model selection. Nevertheless, it is an important, difficult question which priors should be used. We first consider this problem in the context of the one-way random effects model. Arguments based on concepts like orthogonality, matching predictive, and invariance are used to justify a specific form of the priors, where the prior for the new parameter has to be determined. Two different proposals for this proper prior have been derived: the intrinsic priors and the divergence based priors, a recently proposed methodology. It is shown that the divergence based priors produce consistent Bayes factors. The methods are illustrated on examples and compared with other proposals. The method for a general linear mixed model is also explored. (Jointly with Gonzalo Garcia-Donato, University of Valencia, Spain).
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