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      Robust and resistant semivariogram modelling using a generalized bootstrap

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          Abstract

          The bootstrap is a computer-intensive resampling method for estimating the uncertainty of complex statistical models. We expand on an application of the bootstrap for inferring semivariogram parameters and their uncertainty. The model fitted to the median of the bootstrap distribution of the experimental semivariogram is proposed as an estimator of the semivariogram. The proposed application is not restricted to normal data and the estimator is resistant to outliers. Improvements are more significant for data-sets with less than 100 observations, which are those for which semivariogram model inference is the most difficult. The application is illustrated by using it to characterize a synthetic random field for which the true semivariogram type and parameters are known.

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          Optimization by simulated annealing.

          There is a deep and useful connection between statistical mechanics (the behavior of systems with many degrees of freedom in thermal equilibrium at a finite temperature) and multivariate or combinatorial optimization (finding the minimum of a given function depending on many parameters). A detailed analogy with annealing in solids provides a framework for optimization of the properties of very large and complex systems. This connection to statistical mechanics exposes new information and provides an unfamiliar perspective on traditional optimization problems and methods.
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            Robust estimation of the variogram: I

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              Analysis of the Spatial Structure of Properties of Selected Aquifers

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                Author and article information

                Contributors
                Role: ND
                Role: ND
                Role: ND
                Journal
                jsaimm
                Journal of the Southern African Institute of Mining and Metallurgy
                J. S. Afr. Inst. Min. Metall.
                The Southern African Institute of Mining and Metallurgy (Johannesburg, Gauteng, South Africa )
                2225-6253
                2411-9717
                January 2015
                : 115
                : 1
                : 37-44
                S2225-62532015000100010

                This work is licensed under a Creative Commons Attribution 4.0 International License.

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                Figures: 0, Tables: 0, Equations: 0, References: 17, Pages: 8
                Product
                Product Information: SciELO South Africa

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