Incorporating Bayesian Prior Information into CART

• Activity Number: 436
• Type: Contributed
• Date/Time: Thursday, August 12, 2004 : 10:30 AM to 12:20 PM
• Sponsor: Section on Bayesian Statistical Science
• Author(s): Robert Lee*+ and Ming Yin and Eric Harvey and Patrick W. Crockett
• Companies: and Constella Health Sciences and Constella Health Sciences and Constella Health Sciences
• Keywords: CART ; Bayes ; Bayesian

Abstract

The Classification and Regression Tree (CART) algorithm is a hierarchical method for partitioning data into increasingly more homogenous groups. In standard CART analyses, the data drives the rules selected at each splitting node. In some cases, information about the relative importance of the rules may be available from other sources. We propose a Bayesian method which allows the inclusion of such information into CART analyses. Other Bayesian CART methods have been proposed but only allow the inclusion of uniform priors for the splitting rule assignment. We develop a stochastic algorithm for a CART model search which incorporates prior information on the rule importance. A method for placing priors on the tree space is described. Possible permutations of a small tree are summarized for illustrative purposes. We compare the Bayesian CART algorithm with the standard CART algorithm and a CART analysis which includes prior information on the rule importance via a weighting scheme. Including the prior information has a noticeable impact on the rules selected and leads to the reduction of variance for observations belonging to a given terminal node.