Statistics Papers

Document Type

Journal Article

Date of this Version

1-2000

Publication Source

Statistics and Computing

Volume

10

Issue

1

Start Page

17

Last Page

24

DOI

10.1023/A:1008980332240

Abstract

The Bayesian CART (classification and regression tree) approach proposed by Chipman, George and McCulloch (1998) entails putting a prior distribution on the set of all CART models and then using stochastic search to select a model. The main thrust of this paper is to propose a new class of hierarchical priors which enhance the potential of this Bayesian approach. These priors indicate a preference for smooth local mean structure, resulting in tree models which shrink predictions from adjacent terminal node towards each other. Past methods for tree shrinkage have searched for trees without shrinking, and applied shrinkage to the identified tree only after the search. By using hierarchical priors in the stochastic search, the proposed method searches for shrunk trees that fit well and improves the tree through shrinkage of predictions.

Copyright/Permission Statement

The final publication is available at Springer via http://dx.doi.org/ 10.1023/A:1008980332240.

Keywords

binary trees, tree shrinkage, Markov chain Monte Carlo, model selection, stochastic search, mixture models

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Date Posted: 27 November 2017

This document has been peer reviewed.