ANALYTICAL EXPRESSIONS OF CONDITIONAL MEAN, COVARIANCE, AND SAMPLE FUNCTIONS IN GEOSTATISTICS

This work presents analytical expressions for the best estimate, condi tional covariance function, and conditional realizations of a function from sparse observations. In contrast to the prevalent approach in kr iging where the best estimates at every point are determined from the solution of a system of linear equations, the best-estimate function c an be represented analytically in terms of basis functions, whose numb er depends on the observations. This approach is computationally super ior when graphing a function estimate and is also valuable in understa nding what the solution should look like. For example, one can immedia tely see that all ''singularities'' in the best-estimate function are at observation points.