Hierarchical priors for Bayesian CART shrinkage

Hugh Chipman, Edward I. George, Robert E. McCulloch

Research output: Contribution to journalArticle

6 Scopus citations

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.

Original languageEnglish (US)
Pages (from-to)17-24
Number of pages8
JournalStatistics and Computing
Volume10
Issue number1
DOIs
StatePublished - Jan 1 2000
Externally publishedYes

Keywords

  • Binary trees
  • Markov chain Monte Carlo
  • Mixture models
  • Model selection
  • Stochastic search
  • Tree shrinkage

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Statistics and Probability
  • Statistics, Probability and Uncertainty
  • Computational Theory and Mathematics

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