Histogram via entropy reduction (HER): an information-theoretic alternative for geostatistics

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...

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Bibliographic Details
Published in:Hydrology and earth system sciences 2020-09, Vol.24 (9), p.4523-4540
Main Authors: Thiesen, Stephanie, Vieira, Diego M, Mälicke, Mirko, Loritz, Ralf, Wellmann, J. Florian, Ehret, Uwe
Format: Article
Language:English
Subjects:
Agglomeration
Aggregation
Analysis
Data
Empirical analysis
Entropy
Environmental science
Frameworks
Geospatial data
Geostatistics
Histograms
Information theory
Interpolation
Optimization techniques
Probabilistic methods
Probability distribution
Probability theory
Properties
Random variables
Reduction
Spatial analysis
Spatial data
Statistical analysis
Stochasticity
Teaching methods
Uncertainty
Uncertainty analysis
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Summary: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.
ISSN:1607-7938
1027-5606
1607-7938
DOI:10.5194/hess-24-4523-2020