Bayesian Data Fusion for spatial prediction of categorical variables in environmental sciences

Gengler, Sarah [UCL] Bogaert, Patrick [UCL]

(eng) First developed to predict continuous variables, Bayesian Maximum Entropy (BME) has become a complete framework in the context of space-time prediction since it has been extended to predict categorical variables and mixed random fields. This method proposes solutions to combine several sources of data whatever the nature of the information. However, the various attempts that were made for adapting the BME methodology to categorical variables and mixed random fields faced some limitations, as a high computational burden. The main objective of this paper is to overcome this limitation by generalizing the Bayesian Data Fusion (BDF) theoretical framework to categorical variables, which is somehow a simplification of the BME method through the convenient conditional independence hypothesis. The BDF methodology for categorical variables is first described and then applied to a practical case study : the estimation of soil drainage classes using a soil map and point observations in the sandy area of Flanders around the city of Mechelen (Belgium). The BDF approach is compared to BME along with more classical approaches, as Indicator CoKringing (ICK) and logistic regression. Estimators are compared using various indicators, namely the Percentage of Correctly Classified locations (PCC) and the Average Highest Probability (AHP). Although BDF methodology for categorical variables is somehow a simplification of BME approach, both methods lead to similar results and have strong advantages compared to ICK and logistic regression.