Spatial prediction of categorical variables: the Bayesian maximum entropy approach

Abstract.

 Being a non-linear method based on a rigorous formalism and an efficient processing of various information sources, the Bayesian maximum entropy (BME) approach has proven to be a very powerful method in the context of continuous spatial random fields, providing much more satisfactory estimates than those obtained from traditional linear geostatistics (i.e., the various kriging techniques). This paper aims at presenting an extension of the BME formalism in the context of categorical spatial random fields. In the first part of the paper, the indicator kriging and cokriging methods are briefly presented and discussed. A special emphasis is put on their inherent limitations, both from the theoretical and practical point of view. The second part aims at presenting the theoretical developments of the BME approach for the case of categorical variables. The three-stage procedure is explained and the formulations for obtaining prior joint distributions and computing posterior conditional distributions are given for various typical cases. The last part of the paper consists in a simulation study for assessing the performance of BME over the traditional indicator (co)kriging techniques. The results of these simulations highlight the theoretical limitations of the indicator approach (negative probability estimates, probability distributions that do not sum up to one, etc.) as well as the much better performance of the BME approach. Estimates are very close to the theoretical conditional probabilities, that can be computed according to the stated simulation hypotheses.