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Spatial prediction and ordinary kriging. (English) Zbl 0970.86517

Summary: Suppose data \(\{Z(\mathbf s_i)\:i=1,\cdots,n\}\) are observed at spatial locations \(\{\mathbf s_i\:i=1,\cdots,n\}\). From these data, an unknown \(Z(\mathbf s_0)\) is to be predicted at a known location \(\mathbf s _0\), or, if \(Z(\mathbf s_0)\) has a component of measurement error, then a smooth version \(S(\mathbf s_0)\) should be predicted. This article considers the assumptions needed to carry out the spatial prediction using ordinary kriging, and looks at how nugget effect, range, and sill of the variogram affect the predictor. It is concluded that certain commonly held interpretations of these variogram parameters should be modified.

MSC:

86A32 Geostatistics
86-08 Computational methods for problems pertaining to geophysics
86A20 Potentials, prospecting
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