Combining Categorical Information with the Bayesian Maximum Entropy Approach

Abstract

The estimation of categorical variables is a recurrent problem in geostatistics. Beyond traditional and well-known methods like indicator kriging (IK) or classification, the Bayesian Maximum Entropy (BME) approach offers a new sound theoretical framework for modeling the spatial correlation and for computing estimates for categorical variables. In this paper, we show how the BME approach can be used for estimating a categorical variable by combining multiple sources of information. This methodology is illustrated with a practical example dealing with the estimation of soil drainage classes. Data involved consist in a set of punctual observations and a pre-existing exhaustive soil map. Estimates are obtained with BME using various combinations of the data, i.e., (i) the soil map only, (ii) the punctual observations only, and (iii) both of them. For the latter, the relation between the two data sets is taken into account by the way of a double entry probability table when obtaining the maximum entropy joint distribution. The strong advantages of BME over IK are explained at the light of the results that are obtained. The important case of conflicting informations is also discussed at the light of the way BME merges these information.