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 …

Mixtures of Polya tree models provide a flexible alternative when a parametric model may
only hold approximately. I provide computational strategies for obtaining full semiparametric …

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 …

We propose an elementary model for the way in which stochastic perturbations of a
statistical objective function, such as a negative log-likelihood, produce excessive nonlinear …

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 …

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

Ensembles of decision trees are a useful tool for obtaining flexible estimates of regression
functions. Examples of these methods include gradient-boosted decision trees, random …

In applied sciences, generalized linear mixed models have become one of the preferred
tools to analyze a variety of longitudinal and clustered data. Due to software limitations, the …

In the theory of linear models, the concept of degrees of freedom plays an important role.
This concept is often used for measurement of model complexity, for obtaining an unbiased …

In this article, we introduce the BART R package which is an acronym for Bayesian additive
regression trees. BART is a Bayesian nonparametric, machine learning, ensemble …