Measures of Parameter Uncertainty in Geostatistical Estimation and Geostatistical Optimal Design |
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Authors: | Wolfgang Nowak |
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Institution: | (1) Istanbul Technical University Civil Engineering Faculty, Campus Maslak, 34469 Istanbul, Turkey |
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Abstract: | Studies of site exploration, data assimilation, or geostatistical inversion measure parameter uncertainty in order to assess
the optimality of a suggested scheme. This study reviews and discusses measures for parameter uncertainty in spatial estimation.
Most measures originate from alphabetic criteria in optimal design and were transferred to geostatistical estimation. Further
rather intuitive measures can be found in the geostatistical literature, and some new measures will be suggested in this study.
It is shown how these measures relate to the optimality alphabet and to relative entropy. Issues of physical and statistical
significance are addressed whenever they arise. Computational feasibility and efficient ways to evaluate the above measures
are discussed in this paper, and an illustrative synthetic case study is provided. A major conclusion is that the mean estimation
variance and the averaged conditional integral scale are a powerful duo for characterizing conditional parameter uncertainty,
with direct correspondence to the well-understood optimality alphabet. This study is based on cokriging generalized to uncertain
mean and trends because it is the most general representative of linear spatial estimation within the Bayesian framework.
Generalization to kriging and quasi-linear schemes is straightforward. Options for application to non-Gaussian and non-linear
problems are discussed. |
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Keywords: | |
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