geostatistics

Geostatistics is a branch of statistics that focuses on spatial or spatiotemporal data. It aims to model and predict a quantity of interest at unsampled locations by exploiting spatial continuity, often described through the concept of spatial autocorrelation. Central to geostatistics are tools that quantify how similarity decays with distance and that provide not only estimates but also measures of uncertainty.

The variogram or semivariogram summarizes spatial dependence; an empirical variogram is computed from data and fitted with a mathematical model. Kriging uses the variogram model to produce the best linear unbiased predictor at unobserved sites and to quantify prediction variance. Variants include ordinary, simple, and universal kriging, as well as co-kriging, indicator kriging, and regression-kriging. Techniques exist to handle non-stationarity, such as detrending or intrinsic random functions, and to incorporate ancillary information (drift or external variables).

Geostatistics originated in natural resource exploration in the mid-20th century through the work of Danie Krige and Georges Matheron, who formalized the approach. The field has since matured with software packages such as GSLIB, SGeMS, and various R and Python libraries that implement kriging and variogram modeling.

Geostatistics is applied in mining and mineral resource estimation, hydrogeology and groundwater modeling, environmental monitoring, agriculture and soil science, meteorology and climate, and epidemiology. Its strength lies in providing spatially informed estimates and uncertainty assessments from irregularly spaced observations.