Friday, May 16, 2008

Divergence-based priors for the problem of hypothesis testing

Gonzalo García-Donato
(Universidad de Castilla-La Mancha)

Abstract: In the problem of hypothesis testing, a special case of a model selection problem, the solutions obtained under the Bayesian paradigm substantially differ from those obtained within the classical approach. This is one of the reasons why the problem of hypothesis testing and the estimation problem (the model is given) are usually viewed as problems of different nature. On the other hand, it has been repeatedly argued in the literature that the p value does not have a clear interpretation as a measure of evidence against (or in favor of) a hypothesis. The Bayesian solution to the problem of hypothesis testing is based on the posterior probabilities of the hypotheses or equivalently on the Bayes factors. In the objective scenario, where no `external' information is used other than the data, it does not seem to exist an agreement about what prior distributions should be used to derive the Bayes factors. Nevertheless, it is well known that the objective improper prior distributions (like reference priors) for estimation problems cannot be used in hypothesis testing. In this work, we introduce objective proper prior distributions for hypothesis testing and model selection based on measures of divergence between the competing models; we call them divergence based (DB) priors. DB priors have simple forms and desirable properties, like information (finite sample) consistency; often, they are similar to other existing proposals like the intrinsic priors; moreover, in normal linear models scenarios, they exactly reproduce Jeffreys-Zellner-Siow priors. Most importantly, in challenging scenarios such as irregular models and mixture models, the DB priors are well defined and very reasonable, while alternative proposals are not. We derive approximations to the DB priors as well as MCMC and asymptotic expressions for the associated Bayes factors.

Friday, May 16, 2008
Time: 15h30
Room: Sala CTT, Edificio Quelhas, ISEG