Randomized Polya Trees: Bayesian Nonparametrics for Exploration of Multidimensional Structures

Susan Paddock

By comparison with modern parametric Bayesian statistics, practicable and robust methods for exploration and data analysis in nonparametric settings are underdeveloped. The rapid development of non-Bayesian methods and ranges of ad-hoc non-parametric tools for data mining reflect the need for a non-parametric Bayesian approach to exploring and managing data sets in even moderate dimensional problems. I will address this issue by presenting multivariate Polya tree based methods for modeling multidimensional probability distributions. To address partition dependence, a randomized Polya tree is defined and implemented for smoothing discontinuities in predictive distributions. Theoretical implications of this approach are developed. Examples of data analyses and predictions will be provided to highlight issues of Bayesian learning and to motivate future research directions.

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