Computationally Simple Anisotropic Lattice Covariograms

  • Author(s) / Creator(s)
  • 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
  • Subjects / Keywords
  • Type of Item
    Article (Draft / Submitted)
  • DOI
    https://doi.org/10.7939/r3-g6qb-bq70
  • License
    Attribution-NonCommercial 4.0 International