Imperial College of Science Technology and Medicine, London - Department of Mathematics
In this talk we propose a new Bayesian approach to data modeling motivated by the difficulties encountered with some tree-based methods. The Bayesian partition model constructs arbitrarily complex response surfaces over the design space by splitting it into an unknown number of disjoint regions. Within each region the data is assumed to be exchangeable and to come from some simple distribution. Using conjugate priors the marginal likelihoods of the models can be obtained analytically for any proposed partitioning of the space, hugely simplifying the sampling algorithm required to simulate from the posterior of interest. By example we shall show how the partition model can be used for a wide variety of problems including regression, classification and disease mapping.