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Entropy 2013, 15(4), 1464-1485; doi:10.3390/e15041464
Article

Information Theory for Correlation Analysis and Estimation of Uncertainty Reduction in Maps and Models

Received: 19 February 2013; in revised form: 12 April 2013 / Accepted: 15 April 2013 / Published: 22 April 2013
(This article belongs to the Special Issue Applications of Information Theory in the Geosciences)
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Abstract: The quantification and analysis of uncertainties is important in all cases where maps and models of uncertain properties are the basis for further decisions. Once these uncertainties are identified, the logical next step is to determine how they can be reduced. Information theory provides a framework for the analysis of spatial uncertainties when different subregions are considered as random variables. In the work presented here, joint entropy, conditional entropy, and mutual information are applied for a detailed analysis of spatial uncertainty correlations. The aim is to determine (i) which areas in a spatial analysis share information, and (ii) where, and by how much, additional information would reduce uncertainties. As an illustration, a typical geological example is evaluated: the case of a subsurface layer with uncertain depth, shape and thickness. Mutual information and multivariate conditional entropies are determined based on multiple simulated model realisations. Even for this simple case, the measures not only provide a clear picture of uncertainties and their correlations but also give detailed insights into the potential reduction of uncertainties at each position, given additional information at a different location. The methods are directly applicable to other types of spatial uncertainty evaluations, especially where multiple realisations of a model simulation are analysed. In summary, the application of information theoretic measures opens up the path to a better understanding of spatial uncertainties, and their relationship to information and prior knowledge, for cases where uncertain property distributions are spatially analysed and visualised in maps and models.
Keywords: information theory; uncertainty; spatial analysis; geological modelling; mutual information; multivariate conditional entropy information theory; uncertainty; spatial analysis; geological modelling; mutual information; multivariate conditional entropy
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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MDPI and ACS Style

Wellmann, J.F. Information Theory for Correlation Analysis and Estimation of Uncertainty Reduction in Maps and Models. Entropy 2013, 15, 1464-1485.

AMA Style

Wellmann JF. Information Theory for Correlation Analysis and Estimation of Uncertainty Reduction in Maps and Models. Entropy. 2013; 15(4):1464-1485.

Chicago/Turabian Style

Wellmann, J. F. 2013. "Information Theory for Correlation Analysis and Estimation of Uncertainty Reduction in Maps and Models." Entropy 15, no. 4: 1464-1485.


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