Using the Gibbs sampler for conditional simulation of Gaussian-based random fields
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Regionalized variables with discrete distributions are commonly associated with counts of individuals (precious stones in ore deposits, wild animals in ecosystems, trees in forests, etc.), that can be represented by a spatial point process. In this paper, we propose to model the point distribution by a Cox process, i.e., a Poisson point process with a random regionalized intensity. The model is parsimonious and versatile, as it allows fitting the histogram of the count variable, its variogram and madogram. Simulation conditional to data is performed by recourse to iterative algorithms based on the Gibbs sampler. Computer programs are provided for parameter inference and for simulation, and an application to a forestry dataset is presented.