Abstract
This work presents analytical expressions for the best estimate, conditional covariance function, and conditional realizations of a function from sparse observations. In contrast to the prevalent approach in kriging where the best estimates at every point are determined from the solution of a system of linear equations, the best-estimate function can be represented analytically in terms of basis functions, whose number depends on the observations. This approach is computationally superior when graphing a function estimate and is also valuable in understanding what the solution should look like. For example, one can immediately see that all “singularities” in the best-estimate function are at observation points.
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Kitanidis, P.K. Analytical expressions of conditional mean, covariance, and sample functions in geostatistics. Stochastic Hydrol Hydraul 10, 279–294 (1996). https://doi.org/10.1007/BF01581870
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DOI: https://doi.org/10.1007/BF01581870