Exploiting informative priors for Bayesian classification and regression trees

A general method for defining informative priors on statistical models is presented and applied specifically to the space of classification and regression trees. A Bayesian approach to learning such models from data is taken, with the Metropolis- Hastings algorithm being used to approximately sample from the posterior. By only using proposal distributions closely tied to the prior, acceptance probabilities are easily computable via marginal likelihood ratios, whatever the prior used. Our approach is empirically tested by varying (i) the data, (ii) the prior and (iii) the proposal distribution. A comparison with related work is given.