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

Hydrology and earth system sciences, vol. 24, pp. 4523–4540

Abstract

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.

Authors 6

1. Stephanie Thiesen corresponding

   Karlsruhe Institute of Technology

   Affiliation as printed

   Institute of Water Resources and River Basin Management, Karlsruhe Institute of Technology, Karlsruhe, Germany

2. Diego M. Vieira corresponding

   University of Freiburg · Bernstein Center for Computational Neuroscience Freiburg

   Affiliation as printed

   Bernstein Center Freiburg, University of Freiburg, Freiburg, Germany

   Department for Microsystems Engineering, University of Freiburg, Freiburg, Germany

3. Mirko Mälicke corresponding

   Karlsruhe Institute of Technology

   Affiliation as printed

   Institute of Water Resources and River Basin Management, Karlsruhe Institute of Technology, Karlsruhe, Germany

4. Ralf Loritz corresponding

   Karlsruhe Institute of Technology

   Affiliation as printed

   Institute of Water Resources and River Basin Management, Karlsruhe Institute of Technology, Karlsruhe, Germany

5. Florian Wellmann corresponding Aachen Computational Geosciences and Reservoir Engineering

   RWTH Aachen University

   Affiliation as printed

   Computational Geosciences and Reservoir Engineering, RWTH Aachen University, Aachen, Germany

6. Uwe Ehret corresponding

   Karlsruhe Institute of Technology

   Affiliation as printed

   Institute of Water Resources and River Basin Management, Karlsruhe Institute of Technology, Karlsruhe, Germany