Some Aspects of Pola Tree Distributions for Statistical Modelling

Michael Lavine
Duke University

Nov 30 1990

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. Examples are given and the empirical Bayes problem is discussed.


Nonparametric Bayes, Dirichlet Process, Tailfree processes


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