Empirical Bayesian kriging implementation and usage

Abstract

We described the key features of the pragmatic geostatistical methodology aiming at resolving the following drawbacks of classical geostatistical models: assuming that the data is the realization of a stationary process; assuming that the data values are distributed according to Gaussian distribution; describing the data with a single generating model; not accounting for the model uncertainty in prediction; and not supporting coincident data and individual measurement errors. Our variant of empirical Bayesian kriging (EBK) is a fast and reliable solution for both automatic and interactive data interpolation. It can be used for interpolation of very large datasets up to billions of points. The following features are discussed: the informative prior distribution construction and usage; automatic data transformation of the dependent variable into a Gaussian distribution; data subsetting and merging the estimated models; and interpolation over large areas on the earth's surface. We conducted one simulation experiment and two case studies using highly variable data to investigate the EBK predicting quality.

Keywords: Data transformation; Empirical Bayesian kriging; Nonstationarity; Optimization; Principal components; Prior distribution.