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Entropy 2016, 18(11), 409; doi:10.3390/e18110409

Entropy-Based Experimental Design for Optimal Model Discrimination in the Geosciences

1
Institute for Modelling Hydraulic and Environmental Systems (LS3)/SimTech, University of Stuttgart, 70569 Stuttgart, Germany
2
Center for Applied Geoscience, University of Tübingen, 72074 Tübingen, Germany
*
Author to whom correspondence should be addressed.
Academic Editors: Raúl Alcaraz Martínez and Kevin H. Knuth
Received: 30 August 2016 / Revised: 3 November 2016 / Accepted: 14 November 2016 / Published: 17 November 2016
(This article belongs to the Special Issue Applications of Information Theory in the Geosciences)
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Abstract

Choosing between competing models lies at the heart of scientific work, and is a frequent motivation for experimentation. Optimal experimental design (OD) methods maximize the benefit of experiments towards a specified goal. We advance and demonstrate an OD approach to maximize the information gained towards model selection. We make use of so-called model choice indicators, which are random variables with an expected value equal to Bayesian model weights. Their uncertainty can be measured with Shannon entropy. Since the experimental data are still random variables in the planning phase of an experiment, we use mutual information (the expected reduction in Shannon entropy) to quantify the information gained from a proposed experimental design. For implementation, we use the Preposterior Data Impact Assessor framework (PreDIA), because it is free of the lower-order approximations of mutual information often found in the geosciences. In comparison to other studies in statistics, our framework is not restricted to sequential design or to discrete-valued data, and it can handle measurement errors. As an application example, we optimize an experiment about the transport of contaminants in clay, featuring the problem of choosing between competing isotherms to describe sorption. We compare the results of optimizing towards maximum model discrimination with an alternative OD approach that minimizes the overall predictive uncertainty under model choice uncertainty. View Full-Text
Keywords: model choice uncertainty; Bayesian model selection; optimal experimental design; mutual information model choice uncertainty; Bayesian model selection; optimal experimental design; mutual information
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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. (CC BY 4.0).

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Nowak, W.; Guthke, A. Entropy-Based Experimental Design for Optimal Model Discrimination in the Geosciences. Entropy 2016, 18, 409.

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