Kriging

Example of one-dimensional data interpolation by kriging, with credible intervals. Squares indicate the location of the data. The kriging interpolation, shown in red, runs along the means of the normally distributed credible intervals shown in gray. The dashed curve shows a spline that is smooth, but departs significantly from the expected values given by those means.

In statistics, originally in geostatistics, kriging or Kriging (/ˈkriːɡɪŋ/), also known as Gaussian process regression, is a method of interpolation based on Gaussian process governed by prior covariances. Under suitable assumptions of the prior, kriging gives the best linear unbiased prediction (BLUP) at unsampled locations.[1] Interpolating methods based on other criteria such as smoothness (e.g., smoothing spline) may not yield the BLUP. The method is widely used in the domain of spatial analysis and computer experiments. The technique is also known as Wiener–Kolmogorov prediction, after Norbert Wiener and Andrey Kolmogorov.

The theoretical basis for the method was developed by the French mathematician Georges Matheron in 1960, based on the master's thesis of Danie G. Krige, the pioneering plotter of distance-weighted average gold grades at the Witwatersrand reef complex in South Africa. Krige sought to estimate the most likely distribution of gold based on samples from a few boreholes. The English verb is to krige, and the most common noun is kriging. The word is sometimes capitalized as Kriging in the literature.

Though computationally intensive in its basic formulation, kriging can be scaled to larger problems using various approximation methods.

  1. ^ Chung, Sang Yong; Venkatramanan, S.; Elzain, Hussam Eldin; Selvam, S.; Prasanna, M. V. (2019). "Supplement of Missing Data in Groundwater-Level Variations of Peak Type Using Geostatistical Methods". GIS and Geostatistical Techniques for Groundwater Science. Elsevier. pp. 33–41. doi:10.1016/b978-0-12-815413-7.00004-3. ISBN 978-0-12-815413-7. S2CID 189989265.