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We propose a novel "tree-averaging" model that utilizes the ensemble ofclassification and regression trees (CART). Each constituent tree is estimatedwith a subset of similar data. We treat this grouping of subsets as Bayesianensemble trees (BET) and model them as an infinite mixture Dirichlet process.We show that BET adapts to data heterogeneity and accurately estimates eachcomponent. Compared with the bootstrap-aggregating approach, BET shows improvedprediction performance with fewer trees. We develop an efficient estimatingprocedure with improved sampling strategies in both CART and mixture models. Wedemonstrate these advantages of BET with simulations, classification of breastcancer and regression of lung function measurement of cystic fibrosis patients.  Keywords: Bayesian CART; Dirichlet Process; Ensemble Approach; Heterogeneity;Mixture of Trees.

BET: Bayesian Ensemble Trees for Clustering and Prediction in Heterogeneous Data