Using the Gibbs sampler for conditional simulation of Gaussian-based random fields

This article presents models of random fields with continuous univariate distributions that are defined by simple operations on stationary or intrinsic Gaussian fields. Realizations of these models can be conditioned to a set of data by using iterative algorithms based on the Gibbs sampler, while parameter inference relies on the fitting of the sample univariate and bivariate distributions. The proposed models are suited to the description of regionalized variables with a spatial clustering of high or low values, patterns of connectivity and curvilinearity, or an asymmetry in the spatial correlation of indicator variables with respect to the median threshold. The simulation procedure is illustrated by a case study in environmental science dealing with nickel concentrations in the topsoil of a polluted site.