Bayesian prediction of clipped Gaussian random fields

Abstract

This work provides a framework to perform prediction in some types of binary random fields. It is assumed the binary random field is obtained by clipping a Gaussian random field at a fixed level. The model, following a Bayesian approach, is used to map a binary outcome over a bounded region D of the plane: For each location s 0∈D , we compute the optimal predictor of Z( s 0) , 0 or 1, given the binary data from a realization of the random field, and provide measures of prediction uncertainty amenable for binary outcomes. The optimal predictor and the measure of prediction uncertainty are computed through data augmentation using Markov Chain Monte Carlo methods; a less computationally demanding plug-in approach is also described. A brief description of a geostatistical method called indicator kriging is given as well as some of its shortcomings. The prediction ability of the model is illustrated with two simulated binary maps, obtaining satisfactory results, and comparisons between the Bayesian, plug-in, and indicator kriging approaches are given.