HER: an information theoretic alternative for geostatistics

Abstract. Interpolation of spatial data has been regarded in many different forms, varying from deterministic to stochastic, purely data-driven to geostatistical, and parametric to non-parametric methods. In this study, we propose a stochastic, geostatistical estimator which combines information theory with probability aggregation methods for minimizing predictive uncertainty, and predicting distributions directly based on empirical probability. Histogram via entropy reduction (HER) relaxes parametrizations, avoiding the risk of adding information not present in data (or losing available information). It provides a proper framework for uncertainty estimation that takes into account both spatial configuration and data values, while allowing to infer (or introduce) physical properties (continuous or discontinuous characteristics) of the field. We investigate the framework utility using synthetically generated datasets and demonstrate its efficacy in ascertaining the underlying field with varying sample densities and data properties (different spatial correlation distances and addition of noise). HER shows comparable performance with popular benchmark models and 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.