Bayesian data fusion in a spatial prediction context: a general formulation |
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Authors: | P Bogaert D Fasbender |
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Institution: | (1) UCL/AGR0/MILA/ENGE, Université Catholique de Louvain, Croix du Sud 2/16, 1348 Louvain-la-Neuve, Belgium |
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Abstract: | In spite of the exponential growth in the amount of data that one may expect to provide greater modeling and predictions opportunities,
the number and diversity of sources over which this information is fragmented is growing at an even faster rate. As a consequence,
there is real need for methods that aim at reconciling them inside an epistemically sound theoretical framework. In a statistical
spatial prediction framework, classical methods are based on a multivariate approach of the problem, at the price of strong
modeling hypotheses. Though new avenues have been recently opened by focusing on the integration of uncertain data sources,
to the best of our knowledges there have been no systematic attemps to explicitly account for information redundancy through
a data fusion procedure. Starting from the simple concept of measurement errors, this paper proposes an approach for integrating
multiple information processing as a part of the prediction process itself through a Bayesian approach. A general formulation
is first proposed for deriving the prediction distribution of a continuous variable of interest at unsampled locations using
on more or less uncertain (soft) information at neighboring locations. The case of multiple information is then considered,
with a Bayesian solution to the problem of fusing multiple information that are provided as separate conditional probability
distributions. Well-known methods and results are derived as limit cases. The convenient hypothesis of conditional independence
is discussed by the light of information theory and maximum entropy principle, and a methodology is suggested for the optimal
selection of the most informative subset of information, if needed. Based on a synthetic case study, an application of the
methodology is presented and discussed. |
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Keywords: | Data merging Measurement errors Soft information Kriging Entropy |
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