The use of epi-splines to model empirical semivariograms for optimal spatial estimation
Tydingco, Peter M.P., II
Horner, Douglas P.
Royset, Johannes O.
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This research investigates the ability of epi-splines to improve upon current methods of creating empirical semivariograms for use in optimal spatial estimation (OSE). Models utilizing traditional methods of curve fitting for semivariograms (spherical, exponential, and Matérn) used in the spatial estimation process are compared to a proposed model that employs an epi-spline for curve fitting. The resulting semivariograms are then used for kriging to produce spatial estimation using a sparse number of measurements. The epi-spline model improves upon the mean absolute error, mean standard error, and range of errors when compared to traditional methods. However, the comparisons indicate that goodness of fit does not drastically improve the resultant spatial estimation. The benefit of epi-splines, in addition to their ability to more accurately depict the relationship between data points, is their ability to incorporate soft information in the form of constraints and the tighter variance of estimates resulting from their use.
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