Bayesian nonparametric modelling for spatial data using Dirichlet processes

Modelling for spatially referenced data is receiving increased attention in the statistics and the more general scientific literature with applications in, e.g., environmental, ecological and health sciences. Bayesian nonparametric modelling for unknown population distributions, i.e., placing distributions on a space of distributions is also enjoying a resurgence of interest thanks to their amenability to MCMC model fitting. Indeed, both areas benefit from the wide availability of high speed computation. Until very recently, there was no literature attempting to merge them. The contribution of this paper is to provide an overview of this recent effort including some new advances. The nonparametric specifications that underlie this work are generalizations of Dirichlet process mixture models. We attempt to interrelate these various choices either as generalizations or suitable limits. We also offer data analytic comparison among these specifications as well as with customary Gaussian process alternatives.