geostatistikas

Geostatistics is a branch of statistics that deals with spatial or spatiotemporal data. It aims to model geographic dependence and to predict values at unmeasured locations by leveraging the spatial correlation among observed data. It also provides measures of prediction uncertainty and methods for assessing data quality and model fit.

Core concepts include the variogram (or semivariogram), which characterizes how data similarity changes with distance; a second-order stationarity or intrinsic hypothesis; and kriging, a family of best linear unbiased predictors that use the variogram to weight observations. Kriging variants include ordinary kriging, universal (regression) kriging, and simple kriging, chosen according to the presence of trends or known means. Other interpolation methods, such as inverse distance weighting, are often used for comparison.

Geostatistics was developed in the 1960s by Georges Matheron and colleagues to improve ore reserve estimation and environmental modeling. Its foundations were laid in the study of regionalized variables and variograms, and the field has since expanded to Bayesian approaches, spatio-temporal methods, and computer-intensive techniques.

Used in mining and petroleum to estimate ore grades and reserves, in hydrology and environmental science to map contamination and groundwater properties, in agriculture for soil and crop mapping, and in epidemiology for disease risk surfaces. Data requirements include spatial coordinates for samples, measurement values, and appropriate modeling of spatial structure; model validation commonly uses cross-validation and simulation.

Modern developments: Geostatistics now includes Bayesian geostatistics, co-kriging with auxiliary variables, spatio-temporal modeling, and computer-intensive simulation techniques that quantify uncertainty and enable rapid processing of large datasets.