Prediction and Inference for Truncated Spatial Data

Abstract

Spatial data in mining, hydrology, and pollution monitoring commonly have a substantial proportion of zeros. One way to model such data is to suppose that some pointwise transformation of the observations follows the law of a truncated Gaussian random field. This article considers Monte Carlo methods for prediction and inference problems based on this model. In particular, a method for computing the conditional distribution of the random field at an unobserved location, given the data, is described. These results are compared to those obtained by simple kriging and indicator cokriging. Simple kriging is shown to give highly misleading results about conditional distributions; indicator cokriging does quite a bit better but still can give answers that are substantially different from the conditional distributions. A slight modification of this basic technique is developed for calculating the likelihood function for such models, which provides a method for computing maximum likelihood estimates of unknown parameters and Bayesian predictive distributions for values of the process at unobserved locations.