Bayesian Prediction of Transformed Gaussian Random Fields

Abstract

The purpose of this work is to extend the methodology presented in Handock and Stein (1993) for prediction in Gaussian random fields to the case of transformed Gaussian random fields when the transformation is only known to belong to a parametric family. As the optimal predictor, the median of the Bayesian predictive distribution is used since the mean of this distribution does not exist for many commonly used nonlinear transformations. Monte Carlo integration is used for the approximation of the predictive density function, which is easy to implement in this framework. An application to spatial prediction of weekly rainfall amounts in Darwin Australia is presented.