Some Aspects of Polya Tree Distributions for Statistical Modelling

Abstract

Polya tree distributions are defined. They are generalizations of Dirichlet processes that allow for the possibility of putting positive mass on the set of continuous distributions. Predictive and posterior distributions are explained. A canonical construction of a Polya tree is given so that the Polya tree has any desired predictive distribution. Choices of the Polya tree parameters are discussed. Mixtures of Polya trees are defined and examples are given.