Department Seminars

General Information

When: Thursdays from 4:00–4:50 p.m.
Where: 1170 TMCB

Ronald Christensen
University of New Mexico
Department of Mathematics & Statistics

2007-10-04

Parametric Nonparametric Statistics: An Introduction to Mixtures of Finite Polya Trees

Mixtures of Finite Polya Trees provide the basis for an increasingly popular method of performing Bayesian nonparametric analyses. We present an introduction to mixtures of finite Polya trees with an emphasis on their basis as a highly parametric generalization of standard parametric families of distributions. The highly parametric nature of generalization is what makes them appropriate for nonparametric analyses but causes concomitant problems of estimation. These are typically overcome by the use of Bayesian reference priors on the new parameters. Integrating the new parameters over the reference prior is what constitutes the mixture in the name of the procedure. The parameters from the original standard parametric families easily admit both subjective and reference priors.