geostatics

Geostatistics is a branch of statistics that deals with spatial or spatiotemporal data. It provides methods for describing, estimating, and predicting the value of a phenomenon at unsampled locations using information from surrounding samples while explicitly accounting for spatial dependence.

Origin and core ideas: The field was formalized by Georges Matheron in the 1960s, who coined the term geostatistics. The prediction technique kriging arose from early mining work by Danie Krige and was generalized by Matheron and others. Central concepts include spatial autocorrelation and the variogram (or semivariogram), which describes how data similarity changes with distance and is summarized by features such as the nugget, sill, and range.

Modeling and prediction: The standard workflow involves collecting data, computing an experimental variogram, selecting and fitting a variogram model, and performing kriging to estimate values at unsampled sites. Kriging yields a linear predictor that minimizes estimation error under the chosen variogram, and it provides a measure of prediction uncertainty. Variogram estimation, model fitting, and cross-validation are typical steps; several kriging variants exist, including ordinary, universal, and cokriging.

Assumptions and extensions: Geostatistics often assumes second-order or intrinsic stationarity and frequently Gaussian processes, though non-stationary and non-Gaussian approaches exist. Extensions include co-kriging for multivariate data, spatiotemporal geostatistics, Bayesian geostatistics, and conditional or sequential Gaussian simulation to quantify uncertainty with multiple realizations.

Applications: Major uses include mineral resource estimation, hydrogeology and groundwater property mapping, environmental monitoring, agriculture, meteorology, and epidemiology.

Limitations: Dependence on a detectable spatial structure, sensitivity to sampling design, and computational demands for large datasets; non-stationarity can require advanced modeling.