A Natural Nonparametric Generalization of Parametric Statistical Models

• Activity Number: 597
• Type: Invited
• Date/Time: Thursday, August 5, 2010 : 8:30 AM to 10:20 AM
• Sponsor: Section on Bayesian Statistical Science
• Author(s): Timothy Edward Hanson*+
• Companies: University of Minnesota
• Keywords: Polya tree ; survival analysis ; nonparametric ; Bayesian ; Dirichlet process

Abstract

Mixtures of Polya trees (MPTs) provide a robust modeling alternative to other nonparametric approaches, e.g. Dirichlet process mixtures, functional expansions, etc. A key property of the MPT prior is that it is easy to center the MPT at a given parametric family of distributions, facilitating testing the appropriateness of a parametric model or other nonparametric models. MPTs have been successfully applied in many settings including failure time, longitudinal, time series, ROC curve, diagnostic test accuracy, and Rasch models, among many others. This talk provides an introduction to MPT, briefly summarizes some recent applications, and then presents new extensions: dependent Polya tree processes and smoothed multivariate Polya trees. Applications to survival modeling and partially exchangeable random effects illustrate the usefulness of this broad class of prior processes.