Kriging

Kriging, also called Gaussian process regression, is a method of interpolation based on a Gaussian process governed by prior covariances. Under suitable assumptions about the prior it gives the best linear unbiased prediction at locations where no sample was taken, which interpolation based on other criteria such as smoothness, for instance a smoothing spline, may not. It predicts the value of a function at a point as a weighted average of the known values in the neighborhood of that point, and it is closely related to regression analysis. The method began in geostatistics and is widely used in spatial analysis and in computer experiments. Its theory was developed by the French mathematician Georges Matheron in 1960, building on the master's thesis of Danie G. Krige, who plotted distance-weighted average gold grades at the Witwatersrand reef complex in South Africa. The basic formulation is computationally intensive, but approximation methods let it scale to larger problems.