| This paper deals with a
theoretical approach to assessing the effects of parameter estimation
uncertainty both on Kriging estimates and on their
estimated error variance. Although a comprehensive treatment of parameter
estimation uncertainty is covered by full Bayesian Kriging at
the cost of extensive numerical integration, the proposed approach has a wide
field of application, given its relative simplicity. The approach
is based upon a truncated Taylor expansion approximation and, within the limits
of the proposed approximation, the conventional Kriging
estimates are shown to be biased for all variograms, the bias depending upon the
second order derivatives with respect to the parameters
times the variance-covariance matrix of the parameter estimates. A new Maximum
Likelihood (ML) estimator for semi-variogram parameters in
ordinary Kriging, based upon the assumption of a multi-normal distribution of
the Kriging cross-validation errors, is introduced as a
mean for the estimation of the parameter variance-covariance matrix.
Keywords: Kriging, maximum likelihood, parameter estimation, uncertainty |