Objective Priors for Model Selection in One-Way Random Eects Models
Dongchu Sun · 2005
It is broadly accepted that the Bayes factor is a key tool in model selection. Nevertheless, it is an important, dicult and still open question which priors should be used to develop objective (or default) Bayes factors. We consider this problem in the context of the one-way random eects model. Arguments based on concepts like orthogonality, matching predictive, and invariance are used to justify a specific form of the priors, in which the (proper) prior for the new parameter (using Jereys’ terminology) has to be determined. Two dierent proposals for this proper prior have been derived: the intrinsic priors and the divergence based priors, a recently proposed methodology. It will be seen that the divergence based priors produce consistent Bayes factors. The methods are illustrated on examples and compared with other proposals. Finally, the divergence based priors and the associated Bayes factor are derived for the unbalanced case.