Spatial Bayesian nonparametric methods

Abstract

We review nonparametric Bayesian approaches to inference for spatial data. The discussion is organized by increasing level of relaxation of traditional parametric assumptions. We start by considering nonparametric priors for covariance functions in a Gaussian process model. Next we allow for non-Gaussian marginal distributions by introducing Gaussian copulas. Finally, we go fully nonparametric and discuss Dirichlet process mixtures for the coefficients in a kernel convolution, Dirichlet process mixtures of Gaussian processes and spatial stickbreaking priors.