Influence of parameter estimation uncertainty in Kriging: Part 1 - Theoretical development

This paper deals with a theoretical approach to assessing the effects of pa rameter estimation uncertainty both on Kriging estimates and on their estim ated error variance. Although a comprehensive treatment of parameter estima tion uncertainty is covered by full Bayesian Kriging at the cost of extensi ve numerical integration, the proposed approach has a wide field of applica tion. given its relative simplicity. The approach is based upon a truncated Taylor expansion approximation and, within the limits of the proposed appr oximation. the conventional Kriging estimates are shown to be biased for al l variograms, the bias depending upon the second order derivatives with res pect to the parameters times the variance-covariance matrix of the paramete r estimates. A new Maximum Likelihood (ML) estimator for semi-variogram par ameters in ordinary Kriging, based upon the assumption of a multi-normal di stribution of the Kriging cross-validation errors, is introduced as a mean for the estimation of the parameter variance-covariance matrix.