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 nonparametric approach to statistical modeling is appealing because it readily
accommodates non-standard relationships in data. This dissertation is a first step to …

The definition and elementary properties of Polya tree distributions are reviewed. Two
theorems are presented showing that Polya trees can be constructed to concentrate …

We present an introduction to an exciting approach to Bayesian nonparametrics, mixtures of
Polya trees (MPTs). MPTs can be viewed as a simple generalization of standard parametric …

Polya trees (PT) are random probability measures which can assign probability 1 to the set
of continuous distributions for certain specifications of the hyperparameters. This feature …

Since their inception in the 1980s, regression trees have been one of the more widely used
nonparametric prediction methods. Tree-structured methods yield a histogram …

We model the error distribution in the standard linear model as a mixture of absolutely
continuous Polya trees constrained to have median 0. By considering a mixture, we smooth …

Bayesian additive regression trees (BART) is a fully Bayesian approach to modeling with
ensembles of trees. BART can uncover complex regression functions with high-dimensional …

We consider modeling a dependent sequence of random partitions. It is well known in
Bayesian nonparametrics that a random measure of discrete type induces a distribution over …

Pólya trees fix partitions and use random probabilities in order to construct random
probability measures. With quantile pyramids we instead fix probabilities and use random …