NDLI: Empirical Maximum Likelihood Kriging: The General Case

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New Paradigms in Subsurface Prediction: Characterization of the Shallow Subsurface; Implications for Urban Infrastructure and Environmental Assessment

Spatial Statistics for Remote Sensing

Mathematical Geosciences : Volume 37, Issue 4, May 2005

Mathematical Geosciences : Volume 37, Issue 3, April 2005

Mathematical Geosciences : Volume 37, Issue 2, February 2005

Mathematical Geosciences : Volume 37, Issue 1, January 2005

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Mathematical Geosciences : Volume 30

Mathematical Geosciences : Volume 29

Empirical Maximum Likelihood Kriging: The General Case

Content Provider	Springer Nature Link
Author	Pardo Igúzquiza, Eulogio Dowd, Peter A.
Copyright Year	2005
Abstract	Although linear kriging is a distribution-free spatial interpolator, its efficiency is maximal only when the experimental data follow a Gaussian distribution. Transformation of the data to normality has thus always been appealing. The idea is to transform the experimental data to normal scores, krige values in the “Gaussian domain” and then back-transform the estimates and uncertainty measures to the “original domain.” An additional advantage of the Gaussian transform is that spatial variability is easier to model from the normal scores because the transformation reduces effects of extreme values. There are, however, difficulties with this methodology, particularly, choosing the transformation to be used and back-transforming the estimates in such a way as to ensure that the estimation is conditionally unbiased. The problem has been solved for cases in which the experimental data follow some particular type of distribution. In general, however, it is not possible to verify distributional assumptions on the basis of experimental histograms calculated from relatively few data and where the uncertainty is such that several distributional models could fit equally well. For the general case, we propose an empirical maximum likelihood method in which transformation to normality is via the empirical probability distribution function. Although the Gaussian domain simple kriging estimate is identical to the maximum likelihood estimate, we propose use of the latter, in the form of a likelihood profile, to solve the problem of conditional unbiasedness in the back-transformed estimates. Conditional unbiasedness is achieved by adopting a Bayesian procedure in which the likelihood profile is the posterior distribution of the unknown value to be estimated and the mean of the posterior distribution is the conditionally unbiased estimate. The likelihood profile also provides several ways of assessing the uncertainty of the estimation. Point estimates, interval estimates, and uncertainty measures can be calculated from the posterior distribution.
Starting Page	477
Ending Page	492
Page Count	16
File Format	PDF
ISSN	08828121
Journal	Mathematical Geosciences
Volume Number	37
Issue Number	5
e-ISSN	15738868
Language	English
Publisher	Kluwer Academic Publishers-Plenum Publishers
Publisher Date	2005-01-01
Publisher Place	New York
Access Restriction	Subscribed
Subject Keyword	geostatistics spatial interpolation maximum likelihood Bayesian statistics posterior distribution Hydrogeology Math. Applications in Geosciences Geotechnical Engineering Statistics for Engineering, Physics, Computer Science, Chemistry & Geosciences
Content Type	Text
Resource Type	Article
Subject	1900/1901 2600/2601

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