Spatial Prediction of Categorical Variables: The BME Approach

Abstract

Categorical variables often comes naturally and play an important role in environmental studies. Traditionally, they are processed in the geostatistical spatial estimation context using the indicator formalism. However, the indicator approach induces several and serious theoretical and practical problems. Among others, let us mention the inconsistencies and limitations of the linear model of coregionalisation, heavy computational load for taking simultaneously into account several categories, the limited pertinence of a linear predictor, and the incoherence of the predicted probabilities (negative probabilities, probabilities that do not sum up to one, etc.). This paper proposes a nonlinear approach that can be viewed as an extension of the Bayesian Maximum Entropy (BME) methods in the framework of categorical variables. The method is based on a maximum entropy reconstruction of high dimensional probabilities tables that are conditioned on their two-dimensional margins, followed by a conditioning of the table. The superiority of the BME approach over the indicator formalism is investigated both from the theoretical and practical point of views using an example.