Evaluation of Stochastic Geographical Matters: Morphologic Geostatistics, Conditional Sequential Simulation and Geographical Weighted Regression

The aim of this study is to highlight four main stochastic modeling procedures for spatial data within Geographical Information Systems (GIS) which are still unknown by most GIS users: Morphologic Geostatistics (MG), Geographical Weighted Regression (GWR), Conditional Sequential Simulation (CSS) for continuous and categorical variables. Sequential simulation, for instance, is a widely used geostatistical tool for obtaining a set of equiprobable simulated realizations of variables from natural phenomena, conditional to observed data, honoring their spatial distribution and uncertainty. While Gaussian simulation involves the generation of many independent realizations of a Gaussian random field but requiring the transformation of original variables, direct sequential simulation (DSS) has been proposed for simulating directly in the original data space and does not rely on multi-Gaussian assumptions. A generic Pb contamination dataset is used to illustrate the MG and CSS procedures. Major relationships among Kriging estimation, spatial autocorrelation, geographical regression and the missing data issue are also reviewed in the last section.