Submitted in partial fulfilment of the requirements for the degree of Master of Philosophy at Queen Mary, University of London, November 2006Classical tree models represent an attempt to create nonparametric models which
have good predictive powers as well a simple structure readily comprehensible by non-
experts. Bayesian tree models have been created by a team consisting of Chipman,
George and McCulloch and second team consisting of Denison, Mallick and Smith.
Both approaches employ Green's Reversible Jump Markov Chain Monte Carlo tech-
nique to carry out a more e®ective search than the `greedy' methods used classically.
The aim of this work is to evaluate both types of Bayesian tree models from a
Bayesian perspective and compare them
