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More on Spatial Prediction

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Random Fields for Spatial Data Modeling

Part of the book series: Advances in Geographic Information Science ((AGIS))

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Abstract

This chapter begins with linear extensions of kriging that provide higher flexibility and allow relaxing the underlying assumptions on the method. Such generalizations include the application of ordinary kriging to intrinsic random fields that can handle non-stationary data, as well as the methods of regression kriging and universal kriging that incorporate deterministic trends in the linear prediction equation [338]. Cokriging allows combining multivariate information in the prediction equations. Various nonlinear extensions of kriging have also been proposed (indicator kriging, disjunctive kriging) that aim to handle non-Gaussian data.

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Philip Warren Anderson

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Notes

  1. 1.

    A square N × N matrix A is diagonally dominant if \( \left \lvert A_{i,i} \right \rvert > \sum _{j=1, \neq i}^{N} \left \lvert \, A_{i,j}\,\right \rvert \) for all i = 1, …, N.

  2. 2.

    The transformation from a vector to a scalar index is uniquely defined. Equation (11.29) employs the ordering used in Matlab linear indexing.

  3. 3.

    We could normalize the first term by dividing with N as in [368]. In this case, the first component of the precision matrix (11.42a) should also be divided by N.

  4. 4.

    The components of the Laplacian and the Bilaplacian in the orthogonal directions are multiplied by directional coefficients; hence, strictly speaking, the sums over the orthogonal directions are not, strictly speaking, equal to the Laplacian and the Bilaplacian.

  5. 5.

    If these values represents real data, then x is replaced by x .

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Hristopulos, D.T. (2020). More on Spatial Prediction. In: Random Fields for Spatial Data Modeling. Advances in Geographic Information Science. Springer, Dordrecht. https://doi.org/10.1007/978-94-024-1918-4_11

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