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

By Ezio Todini. 2001

48 citations recorded by the source corpus.

Abstract. 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

Subfields: Environmental Engineering, Management Science and Operations Research, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/876c610b11ff411fa187b7847db6d9f4063e64c2

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In Environmental Engineering

In Management Science and Operations Research

In Statistics and Probability

Citations in the corpus

Optimized Sample Schemes for Geostatistical Surveys (2007, background): “Todini (2001) and Zimmerman and Cressie (1992) have combined the inverse Fisher Information matrix with a further Taylor series to demonstrate how ordinary kriging errors propagate from variogram errors.”