Bayesian nonparametric binary regression via random tessellations

A Bayesian nonparametric model for binary random variables is introduced. The characterization of the probability model is based on the Dirichlet process and on the Poisson hyperplane tessellation model. These two stochastic models are combined in order to adapt, under the hypothesis of partial exchangeability, the reinforcement mechanism of the Pólya urn scheme. A Gibbs sampling algorithm for implementing predictive inference is illustrated and an application of the inferential procedure is discussed.