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Computationally Simple Anisotropic Lattice Covariograms
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- Author(s) / Creator(s)
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When working with contemporary spatial ecological datasets, statistical
modellers are often confronted by two major challenges: (I) the need for covariance
models with the flexibility to accomodate directional patterns of anisotropy; and
(II) the computational effort demanded by high-dimensional inverse and determinant
problems involving the covariance matrix ® +. In the case of rectangular lattice data, the
spatially separable covariogram is a longstanding but underused model that can reduce
arithmetic complexity by orders of magnitude. We examine a class of covariograms
for stationary data that extends the separable model through affine coordinate transformations,
providing a far greater flexibility for handling anisotropy than that offered
by the standard approach of using geometric anisotropy to extend an isotropic model.
This motivates our development of an extremely fast estimator of the orientation of
the axes of range anisotropy on spatial lattice data, and a powerful visual diagnostic
for nonstationarity. In a case study, we demonstrate how these tools can be used to
analyze and predict forest damage patterns caused by outbreaks of the mountain pine
beetle. -
- Date created
- 2020-07-31
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- Subjects / Keywords
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- Type of Item
- Article (Draft / Submitted)