Spring 2009 Thursday, March 26   Speaker: Ruitao Liu Department of Statistics The University of Florida Title: "On Some New Contributions Towards Objective Priors" Abstract: Bayesian methods are gaining increasing popularity in the theory and practice of statistics. One key component in Bayesian inference is the selection of priors. Generally speaking, there are two classes of priors: subjective priors and objective priors. With enough historical data, it is often possible to elicit a suitable subjective prior. But even in its absence, Bayesian methods can often be very effective by the use of so-called 'objective' priors. In this talk, I will give a selective review of objective priors and talk about two new contributions towards objective priors 'General Divergence Priors' and 'Moment Matching Priors'. For General Divergence criterion, the goal is to find some 'objective' prior by approximate maximization of the divergence between the prior and the posterior under a general divergence criterion which includes the Kullback-Leibler, Bhattacharyya-Hellinger and Chisquare divergence. The maximization is based on an asymptotic expansion of this divergence. It is shown that with the exception of one particular case, namely the chi-square divergence, the general divergence criterion yields Jeffreys' prior. For the Moment Matching criterion, it requires the matching of the posterior mean with the Maximum likelihood estimator up to a high order of approximation. A complete characterization of such priors in the one- or multi-parameter case is provided.

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