On the equivalence of kriging and maximum entropy estimators |
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Authors: | Yuh-Ming Lee and J Hugh Ellis |
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Institution: | (1) Graduate Institute of Natural Resources Management, National Chung Hsing University, Taipei, Taiwan, Republic of China;(2) Department of Geography and Environmental Engineering, The Johns Hopkins University, 34th & Charles Street, 21218 Baltimore, Maryland |
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Abstract: | This study compares kriging and maximum entropy estimators for spatial estimation and monitoring network design. For second-order
stationary random fields (a subset of Gaussian fields) the estimators and their associated interpolation error variances are
identical. Simple lognormal kriging differs from the lognormal maximum entropy estimator, however, in both mathematical formulation
and estimation error variances. Two numerical examples are described that compare the two estimators. Simple lognormal kriging
yields systematically higher estimates and smoother interpolation surfaces compared to those produced by the lognormal maximum
entropy estimator. The second empirical comparison applies kriging and entropy-based models to the problem of optimizing groundwater
monitoring network design, using six alternative objective functions. The maximum entropy-based sampling design approach is
shown to be the more computationally efficient of the two. |
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Keywords: | spatial estimation entropy kriging monitoring network design lognormal random fields |
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