Abstract
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.
Highlights
Spatial interpolation methods are useful tools for filling gaps in data
There is a broad range of methods available that have been considered in many different forms, from simple approaches, such as nearest neighbor (NN; Fix and Hodges, 1951) and inverse distance weighting (IDW; Shepard, 1968), to geostatistical and, more recently, machine-learning methods
We show that its potential goes beyond prediction since, by construction, Histogram via entropy reduction (HER) allows inferring of or introducing physical properties of a field under study and provides a proper framework for uncertainty prediction, which takes into account the spatial configuration and the data values
Summary
Spatial interpolation methods are useful tools for filling gaps in data. Since information of natural phenomena is often collected by point sampling, interpolation techniques are essential and required for obtaining spatially continuous data over the region of interest (Li and Heap, 2014). There is a broad range of methods available that have been considered in many different forms, from simple approaches, such as nearest neighbor (NN; Fix and Hodges, 1951) and inverse distance weighting (IDW; Shepard, 1968), to geostatistical and, more recently, machine-learning methods Stochastic geostatistical approaches, such as ordinary kriging (OK), have been widely studied and applied in various disciplines since their introduction to geology and mining by Krige (1951), bringing significant results in the context of environmental sciences. OK uses fitted functions to offer uncertainty estimates, while deterministic estimators (NN and IDW) avoid function parameterizations at the cost of neglecting uncertainty analysis In this sense, researchers are confronted with the trade-off between avoiding parameterization assumptions and obtaining uncertainty results (stochastic predictions)
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