Non-Gaussian Bayesian Geostatistical Modeling

Abstract

Sampling models for geostatistical data are usually based on Gaussian processes. However, real data often display non-Gaussian features, such as heavy tails. In this article we propose a more flexible class of sampling models. We start from the spatial linear model that has a spatial trend plus a stationary Gaussian error process. We extend the sampling model to non-Gaussianity by including a scale parameter at each location. We make sure that we obtain a valid stochastic process. The scale parameters are spatially correlated to ensure that the process is mean square continuous. We derive expressions for the moments and the kurtosis of the process. This more general stochastic process allows us to accommodate and identify observations that would be outliers under a Gaussian sampling process. For the spatial correlation structure, we adopt the flexible Matèrn class with unknown smoothness parameter. Furthermore, a nugget effect is included in the model. Bayesian inference (posterior and predictive) is performed using a Markov chain Monte Carlo algorithm. The choice of the prior distribution is discussed and its importance assessed in a sensitivity analysis. We also examine identifiability of the parameters. Our methods are illustrated with two datasets.