Randomized Polya tree models for nonparametric Bayesian inference

Like other partition-based models, Polya trees suffer the problem of partition dependence. We develop Randomized Polya Trees to address this limitation. This new framework inherits the structure of Polya trees but "jitters" partition points and as a result smooths discontinuities in predictive distributions. Some of the theoretical aspects of the new framework are developed, followed by discussion of methodological and computational issues arising in implementation. Examples of data analyses and prediction problems are provided to highlight issues of Bayesian inference in this context.