Influence of parameter estimation uncertainty in Kriging

被引:17
作者
Todini, E
Ferraresi, M
机构
[1] Institute for Hydraulic Construction, University of Bologna, 40136 Bologna
关键词
D O I
10.1016/S0022-1694(96)80024-2
中图分类号
TU [建筑科学];
学科分类号
0813 ;
摘要
This paper deals with a theoretical approach to assessing the effects of parameter estimation uncertainty on both Kriging estimates and their estimated error variance, by no longer considering the variogram parameter estimates as fixed values (as is conventionally done) but rather as realisations of random variables, the true values of which are unknown. By means of a second-order Taylor expansion, an approximate expression for the Kriging estimates is obtained as a function of the parameter estimates; subsequently, by taking expectations, an approximation both for the expected value of the Kriging estimates and for their variance is obtained. A maximum likelihood estimator for the parameters is also formulated, which allows for estimating the variance covariance matrix of the parameters as the inverse of the Fisher information matrix. Within the limits of the proposed approximation, the conventional Kriging estimates are shown to be biased for all variograms, the bias depending upon the Kriging interpolating weights' second-order derivatives with respect to the parameters times the variance-covariance matrix of the parameters (both functions of the variogram model adopted). Moreover, the conventional Kriging variance estimate is always underestimated by a factor which depends upon its second-order derivatives with respect to the parameters times the variance-covariance matrix of the parameters. This underestimation not only modifies the spatial distribution of the Kriging variance, but may also induce the adoption of the wrong model, given that the choice of a specific variogram is generally performed by comparing the Kriging variances generated by the different models.
引用
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页码:555 / 566
页数:12
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