Information Theory for Correlation Analysis and Estimation of Uncertainty Reduction in Maps and Models
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 framewor...
Main Author: | |
---|---|
Format: | Article |
Language: | English |
Published: |
MDPI AG
2013-04-01
|
Series: | Entropy |
Subjects: | |
Online Access: | http://www.mdpi.com/1099-4300/15/4/1464 |
id |
doaj-4a04eaf0592946aebb03fe84780b6269 |
---|---|
record_format |
Article |
spelling |
doaj-4a04eaf0592946aebb03fe84780b62692020-11-25T02:26:51ZengMDPI AGEntropy1099-43002013-04-011541464148510.3390/e15041464Information Theory for Correlation Analysis and Estimation of Uncertainty Reduction in Maps and ModelsJ. Florian WellmannThe 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.http://www.mdpi.com/1099-4300/15/4/1464information theoryuncertaintyspatial analysisgeological modellingmutual informationmultivariate conditional entropy |
collection |
DOAJ |
language |
English |
format |
Article |
sources |
DOAJ |
author |
J. Florian Wellmann |
spellingShingle |
J. Florian Wellmann Information Theory for Correlation Analysis and Estimation of Uncertainty Reduction in Maps and Models Entropy information theory uncertainty spatial analysis geological modelling mutual information multivariate conditional entropy |
author_facet |
J. Florian Wellmann |
author_sort |
J. Florian Wellmann |
title |
Information Theory for Correlation Analysis and Estimation of Uncertainty Reduction in Maps and Models |
title_short |
Information Theory for Correlation Analysis and Estimation of Uncertainty Reduction in Maps and Models |
title_full |
Information Theory for Correlation Analysis and Estimation of Uncertainty Reduction in Maps and Models |
title_fullStr |
Information Theory for Correlation Analysis and Estimation of Uncertainty Reduction in Maps and Models |
title_full_unstemmed |
Information Theory for Correlation Analysis and Estimation of Uncertainty Reduction in Maps and Models |
title_sort |
information theory for correlation analysis and estimation of uncertainty reduction in maps and models |
publisher |
MDPI AG |
series |
Entropy |
issn |
1099-4300 |
publishDate |
2013-04-01 |
description |
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. |
topic |
information theory uncertainty spatial analysis geological modelling mutual information multivariate conditional entropy |
url |
http://www.mdpi.com/1099-4300/15/4/1464 |
work_keys_str_mv |
AT jflorianwellmann informationtheoryforcorrelationanalysisandestimationofuncertaintyreductioninmapsandmodels |
_version_ |
1724845357491290112 |