Histogram via entropy reduction (HER): an information-theoretic alternative for geostatistics
<p>Interpolation of spatial data has been regarded in many different forms, varying from deterministic to stochastic, parametric to nonparametric, and purely data-driven to geostatistical methods. In this study, we propose a nonparametric interpolator, which combines information theory with pr...
| Main Authors: | , , , , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Copernicus Publications
2020-09-01
|
| Series: | Hydrology and Earth System Sciences |
| Online Access: | https://hess.copernicus.org/articles/24/4523/2020/hess-24-4523-2020.pdf |
| _version_ | 1818278171976400896 |
|---|---|
| author | S. Thiesen D. M. Vieira D. M. Vieira M. Mälicke R. Loritz J. F. Wellmann U. Ehret |
| author_facet | S. Thiesen D. M. Vieira D. M. Vieira M. Mälicke R. Loritz J. F. Wellmann U. Ehret |
| author_sort | S. Thiesen |
| collection | DOAJ |
| description | <p>Interpolation of spatial data has been regarded in many different forms, varying from deterministic to stochastic, parametric to nonparametric, and purely data-driven to geostatistical methods. In this study, we propose a nonparametric interpolator, which combines information theory with probability aggregation methods in a geostatistical framework for the stochastic estimation of unsampled points. Histogram via entropy reduction (HER) predicts conditional distributions based on empirical
probabilities, relaxing parameterizations and, therefore, avoiding the risk of adding information not present in data. By construction, it provides a proper framework for uncertainty estimation since it accounts for both
spatial configuration and data values, while allowing one to introduce or infer properties of the field through the aggregation method. We investigate the framework using synthetically generated data sets and demonstrate its efficacy in ascertaining the underlying field with varying sample densities and data properties. HER shows a comparable performance to popular benchmark models, with the additional advantage of higher generality. The novel method brings a new perspective of spatial interpolation and uncertainty analysis to geostatistics and statistical learning, using the lens of information theory.</p> |
| first_indexed | 2024-12-12T23:13:12Z |
| format | Article |
| id | doaj.art-d50bb6a9c07f4b1eba42ec28b30740a7 |
| institution | Directory Open Access Journal |
| issn | 1027-5606 1607-7938 |
| language | English |
| last_indexed | 2024-12-12T23:13:12Z |
| publishDate | 2020-09-01 |
| publisher | Copernicus Publications |
| record_format | Article |
| series | Hydrology and Earth System Sciences |
| spelling | doaj.art-d50bb6a9c07f4b1eba42ec28b30740a72022-12-22T00:08:33ZengCopernicus PublicationsHydrology and Earth System Sciences1027-56061607-79382020-09-01244523454010.5194/hess-24-4523-2020Histogram via entropy reduction (HER): an information-theoretic alternative for geostatisticsS. Thiesen0D. M. Vieira1D. M. Vieira2M. Mälicke3R. Loritz4J. F. Wellmann5U. Ehret6Institute of Water Resources and River Basin Management, Karlsruhe Institute of Technology, Karlsruhe, GermanyDepartment for Microsystems Engineering, University of Freiburg, Freiburg, GermanyBernstein Center Freiburg, University of Freiburg, Freiburg, GermanyInstitute of Water Resources and River Basin Management, Karlsruhe Institute of Technology, Karlsruhe, GermanyInstitute of Water Resources and River Basin Management, Karlsruhe Institute of Technology, Karlsruhe, GermanyComputational Geosciences and Reservoir Engineering, RWTH Aachen University, Aachen, GermanyInstitute of Water Resources and River Basin Management, Karlsruhe Institute of Technology, Karlsruhe, Germany<p>Interpolation of spatial data has been regarded in many different forms, varying from deterministic to stochastic, parametric to nonparametric, and purely data-driven to geostatistical methods. In this study, we propose a nonparametric interpolator, which combines information theory with probability aggregation methods in a geostatistical framework for the stochastic estimation of unsampled points. Histogram via entropy reduction (HER) predicts conditional distributions based on empirical probabilities, relaxing parameterizations and, therefore, avoiding the risk of adding information not present in data. By construction, it provides a proper framework for uncertainty estimation since it accounts for both spatial configuration and data values, while allowing one to introduce or infer properties of the field through the aggregation method. We investigate the framework using synthetically generated data sets and demonstrate its efficacy in ascertaining the underlying field with varying sample densities and data properties. HER shows a comparable performance to popular benchmark models, with the additional advantage of higher generality. The novel method brings a new perspective of spatial interpolation and uncertainty analysis to geostatistics and statistical learning, using the lens of information theory.</p>https://hess.copernicus.org/articles/24/4523/2020/hess-24-4523-2020.pdf |
| spellingShingle | S. Thiesen D. M. Vieira D. M. Vieira M. Mälicke R. Loritz J. F. Wellmann U. Ehret Histogram via entropy reduction (HER): an information-theoretic alternative for geostatistics Hydrology and Earth System Sciences |
| title | Histogram via entropy reduction (HER): an information-theoretic alternative for geostatistics |
| title_full | Histogram via entropy reduction (HER): an information-theoretic alternative for geostatistics |
| title_fullStr | Histogram via entropy reduction (HER): an information-theoretic alternative for geostatistics |
| title_full_unstemmed | Histogram via entropy reduction (HER): an information-theoretic alternative for geostatistics |
| title_short | Histogram via entropy reduction (HER): an information-theoretic alternative for geostatistics |
| title_sort | histogram via entropy reduction her an information theoretic alternative for geostatistics |
| url | https://hess.copernicus.org/articles/24/4523/2020/hess-24-4523-2020.pdf |
| work_keys_str_mv | AT sthiesen histogramviaentropyreductionheraninformationtheoreticalternativeforgeostatistics AT dmvieira histogramviaentropyreductionheraninformationtheoreticalternativeforgeostatistics AT dmvieira histogramviaentropyreductionheraninformationtheoreticalternativeforgeostatistics AT mmalicke histogramviaentropyreductionheraninformationtheoreticalternativeforgeostatistics AT rloritz histogramviaentropyreductionheraninformationtheoreticalternativeforgeostatistics AT jfwellmann histogramviaentropyreductionheraninformationtheoreticalternativeforgeostatistics AT uehret histogramviaentropyreductionheraninformationtheoreticalternativeforgeostatistics |