Statistics Papers

Document Type

Journal Article

Date of this Version

2010

Publication Source

Annals of Applied Statistics

Volume

4

Issue

1

Start Page

266

Last Page

298

DOI

10.1214/09-AOAS285

Abstract

We develop a Bayesian “sum-of-trees” model where each tree is constrained by a regularization prior to be a weak learner, and fitting and inference are accomplished via an iterative Bayesian backfitting MCMC algorithm that generates samples from a posterior. Effectively, BART is a nonparametric Bayesian regression approach which uses dimensionally adaptive random basis elements. Motivated by ensemble methods in general, and boosting algorithms in particular, BART is defined by a statistical model: a prior and a likelihood. This approach enables full posterior inference including point and interval estimates of the unknown regression function as well as the marginal effects of potential predictors. By keeping track of predictor inclusion frequencies, BART can also be used for model-free variable selection. BART’s many features are illustrated with a bake-off against competing methods on 42 different data sets, with a simulation experiment and on a drug discovery classification problem.

Keywords

Bayesian backfitting, boosting, CART, classification, ensemble, MCMC, nonparametric regression, probit model, random basis, regularizatio, sum-of-trees model, variable selection, weak learner

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Date Posted: 27 November 2017

This document has been peer reviewed.