) Spatial prediction of soil properties: the Bayesian Maximum Entropy approach
Soil properties play important roles in a lot of environmental issues like diffuse pollution, erosion hazards or precision agriculture. With the developments of soil process models and geographical information systems, the need for accurate knowledge about soil properties becomes more acute. However, while the sources of information become each year more numerous and diversified, they rarely provide us with data at the same time having the required level of spatial and attribute accuracy. An important challenge thus consists in combining those data sources at best so as to meet the high accuracy requirements.
The Bayesian Maximum Entropy (BME) approach appears as a potential candidate for achieving this task: it is especially designed for managing simultaneously data of various nature and quality ("hard" and "soft" data, continuous or categorical). It relies on a two-steps procedure involving an objective way for obtaining a prior distribution in accordance with the general knowledge at hand (the ME part), and a Bayesian conditionalization step for updating this prior probability distribution function (pdf) with respect to the specific data collected on the study site. At each prediction location, an entire pdf is obtained, allowing subsequently the easy computation of elaborate statistics chosen for their adequacy with the objectives of the study.
In this thesis, the theory of BME is explained in a simplified way using standard probabilistic notations. The recent developments towards categorical variables are incorporated and an attempt is made to formulate a unified framework for both categorical and continuous variables, thus emphasizing the generality and flexibility of the BME approach.
The potential of the method for predicting continuous variables is then illustrated by a series of studies dealing with the soil texture fractions (sand, silt and clay). For the categorical variables, a case study focusing on the prediction of the status of the water table is presented. The use of multiple and sometimes contradictory data sources is also analyzed.
Throughout the document, BME is compared to classic geostatistical techniques like simple, ordinary or indicator kriging. Thorough discussions point out the inconsistencies of those methods and explain how BME is solving the problems.
Rather than being but another geostatistical technique, BME has to be considered as a knowledge processing approach. With BME, practitioners will find a valuable tool for analyzing their spatio-temporal data sets and for providing the stake-holders with accurate information about the environmental issues to which they are confronted.