A Bayesian Approach For CART

A Bayesian approach for finding classification and regression tree (CART) models is proposed. By putting an appropriate prior distribution on the · space of CART models, the resulting posterior will put higher probability on the more "promising trees". In particular, priors are proposed which penalize complexity by putting higher probability on trees with fewer nodes. Metropolis-Hastings algorithms are used to rapidly grow trees in such a way that the high posterior probability trees are more likely to be obtained. In effect, the algorithm performs a stochastic search for promising trees. Examples are used to illustrate the potential superiority of this approach over conventional greedy methods.