Bayesian data fusion in environmental sciences : theory and applications

During the last thirty years, new technologies have contributed to a drastic increase of the amount of data in environmental sciences. Monitoring networks, remote sensors, archived maps and large databases are just few examples of the possible information sources responsible for this growing amount of information. For obvious reasons, it might be interesting to account for all these information when dealing with a space-time prediction/estimation context. In environmental sciences, measurements are very often sampled scarcely over space and time. Geostatistics is the field that investigates variables in a space-time context. It includes a large number of methods and approaches that all aim at providing space-time predictions (or interpolations) for variables scarcely known in space and in time by accounting for space-time dependance between these variables. As a consequence, geostatistics methods are relevant when dealing with the processing and the analysis of environmental variables in which space and time play an important role. As direct consequence of the increasing amount of data, there is an important diversity in the information (e.g. different nature, different uncertainty). These issues have recently motivated the emergence of the concept of data fusion. Broadly speaking, the main objective of data fusion methods is to deal with various information sources in such a way that the final result is a single prediction that accounts for all the sources at once. This enables thus to conciliate several and potentially contradictory sources instead of having to select only one of them because of a lack of appropriate methodology. For most of existing geostatistics methods, it is quite difficult to account for a potentially large number of different information sources at once. As a consequence, one has often to opt for only one information source among all the available sources. This of course leads to a dramatic loss of information. In order to avoid such choices, it is thus relevant to get together the concepts of both data fusion and geostatistics in the context of environmental sciences. The objectives of this thesis are (i) to develop the theory of a Bayesian data fusion (BDF) framework in a space-time prediction context and (ii) to illustrate how the proposed BDF framework can account for a diversity of information sources in a space-time context. The method will thus be applied to a few environmental sciences applications for which (i) crucial available information sources are typically difficult to account for or (ii) the number of secondary information sources is a limitation when using existing methods. Reproduced by permission of Springer. P. Bogaert and D. Fasbender (2007). Bayesian data fusion in a spatial prediction context: a general formulation. Stoch. Env. Res. Risk. A. , vol. 21, 695-709. (Chap. 1). © 2008 IEEE. Reprinted, with permission, from D. Fasbender, J. Radoux and P. Bogaert (2008). Bayesian data fusion for adaptable image pansharpening. IEEE Trans. Geosci. Rem. Sens. , vol. 46, 1847-1857. (Chap. 3). © 2008 IEEE. Reprinted, with permission, from D. Fasbender, D. Tuia, P. Bogaert and M. Kanevski (2008). Support-based implementation of Bayesian data fusion for spatial enhancement: applications to ASTER thermal images. IEEE Geosci. Rem. Sens. Letters, vol. 6, 598-602. (Chap. 4). Reproduced by permission of American Geophysical Union. D. Fasbender, L. Peeters, P. Bogaert and A. Dassargues (2008). Bayesian data fusion applied to water table spatial mapping. Accepted for publication in Water Resour. Res. (Chap. 5)