Bayesian prediction of transformed Gaussian random fields

A model for prediction in some types of non-Gaussian random fields is presented. It extends the work of Handcock and Stein to prediction in transformed Gaussian random fields, where the transformation is known to belong to a parametric family of monotone transformations. The Bayesian transformed Gaussian model (BTG) provides an alternative to trans-Gaussian kriging taking into account the major sources of uncertainty, including uncertainty about the "normalizing transformation" itself, in the computation of the predictive density function. Unlike trans-Gaussian kriging, this approach mitigates the consequences of a misspecified transformation, giving in this sense a more robust predictive inference. Because the mean of the predictive distribution does not exist for some commonly used families of transformations, the median is used as the optimal predictor. The BTG model is applied in the spatial prediction of weekly rainfall amounts. Cross-validation shows the predicting performance of the BTG model compares favorably with several kriging variants.