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Spatial Prediction Fundamentals

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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

The analysis of spatial data involves different procedures that typically include model estimation, spatial prediction, and simulation. Model estimation or model inference refers to determining a suitable spatial model and the “best” values for the parameters of the model. Parameter estimation is not necessary for certain simple deterministic models (e.g., nearest neighbor method), since such models do not involve any free parameters. Model selection is then used to choose the “optimal model” (based on some specified statistical criterion) among a suite of candidates.

To boldly go where no data have gone before, to seek out plausible trends and fluctuations.

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Notes

  1. 1.

    This statement is clarified in the section on kriging.

  2. 2.

    The reference [711] does not include the constant, dimension-dependent coefficients of the biharmonic Green functions given in (10.9). This is not an issue for MCI, since constant factors are automatically compensated by the weights w n.

  3. 3.

    A hyper-surface is a manifold of dimension d − 1 embedded in an ambient space of dimension d.

  4. 4.

    In mathematics, the term “space” refers to a set with some specified rules that impose structure.

  5. 5.

    In full detail, the condition on the spectral density’s tail allows for a product between an algebraic function ∥kα and a slowly varying function of k, i.e., combinations of the form \(\|\mathbf {k}\|{ }^{-\alpha } \ln \|\mathbf {k}\|\). However, such spectral densities are not typically used.

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Hristopulos, D.T. (2020). Spatial Prediction Fundamentals. In: Random Fields for Spatial Data Modeling. Advances in Geographic Information Science. Springer, Dordrecht. https://doi.org/10.1007/978-94-024-1918-4_10

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