Bayesian Partitioning for Classification and Regression

In this paper we propose a new Bayesian approach to data modelling. The Bayesian partition model constructs arbitrarily complex regression and classification surfaces by splitting the design space 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 where the number and location of the regions is assumed unknown a priori. Markov chain Monte Carlo simulation techniques are used to obtain distributions on partition structures and by averaging across samples smooth prediction surfaces are formed. Keywords: Bayesian linear model; classification; Markov chain Monte Carlo (MCMC); regression; Voronoi tessellation. 1 Introduction Regression and classification are among the most widely researched problems in statistics. However, their importance in science spreads over m..