geostatistikat

Geostatistikat, often called geostatistics, is a branch of statistics that analyzes spatially referenced data and makes predictions for unsampled locations. It explicitly models spatial dependence—the idea that observations closer in space tend to be more alike—and uses this structure to estimate values and quantify uncertainty across a region or over time.

Its core tools include the variogram (or semivariogram), which summarizes how data similarity changes with distance, and kriging, a family of linear unbiased predictors that use the variogram and observed values. Different kriging variants exist, such as ordinary, universal, simple, and indicator kriging, as well as co-kriging when auxiliary variables are available. Geostatistics also employs stochastic simulation, Bayesian methods, and Gaussian-process models to characterize uncertainty and generate multiple plausible realizations.

Applications span resource estimation in mining and petroleum, hydrogeology and groundwater management, environmental contamination mapping, soil science, agriculture, and epidemiology. It is used to interpolate measurements, optimize sampling schemes, and assess risk and decision-making under spatial uncertainty.

Geostatistics emerged in mining in the mid-20th century from the work of Danie Krige and Georges Matheron. It is implemented in software such as gstat and geoR in R, PyKrige and gstools in Python, and various GIS packages.

Limitations include assumptions of stationarity and isotropy, data sparsity, and computational demands for large datasets. Modern approaches address non-stationarity through detrending, local kriging, or non-stationary Gaussian processes and integrate covariates from remote sensing and environmental data.