Kriging predicts a spatial random field by a linear combination of observations chosen to minimize prediction variance subject to the appropriate mean constraints. Its different forms depend on whether the mean is known, an unknown constant, or an unknown regression drift.
For unknown drift , a full-column-rank design matrix , a known positive-definite matrix observation covariance matrix , and target drift row , universal kriging minimizes prediction variance subject to . Equivalently, with , predict . The first term is the estimated trend alone; the second is a correlated residual prediction.
For an unknown constant mean, ordinary kriging minimizes error variance subject to weights summing to one. This unbiasedness constraint distinguishes it from simple kriging.
For known zero mean, invertible observation covariance , target covariance vector and target variance , simple kriging predicts with error variance . Completing the covariance quadratic form proves optimality. A multivariate normal distribution makes this the exact conditional mean and variance.
Articles by others on the same topic
Kriging is a statistical interpolation technique used extensively in geostatistics, spatial analysis, and various fields such as mining, environmental science, and agriculture. It allows for the estimation of unknown values at specific locations based on known data points, taking into account both the distance and the spatial arrangement of the points. Developed by the South African engineer Danie G. Krige in the 1950s, Kriging uses a method based on the spatial correlation of the data.