Polya tree priors and their estimation with multi-group data

The purpose of this article is in twofold. Firstly, we present new and weaker conditions under which a tail-free or a Polya tree prior can sit on the collection of absolutely continuous probabilities with respect to certain probability measure. Second, we investigate the empirical Bayesian (EB) estimation of the parameters of Polya tree priors with multi-group data. Two types of EB estimates, maximum likelihood estimates and moment estimates, are discussed. We also make an exploratory analysis on the estimability of the parameters and the distribution of the number of estimable parameters.