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Inverses of Matérn covariances on grids
[Spatial modeling with R-INLA: A review]

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  • Joseph Guinness

Abstract

SummaryWe conduct a study of the aliased spectral densities of Matérn covariance functions on a regular grid of points, elucidating the properties of a popular approximation based on stochastic partial differential equations. While other researchers have shown that this approximation can work well for the covariance function, we find that it assigns too much power at high frequencies and does not provide increasingly accurate approximations to the inverse as the grid spacing goes to zero, except in the one-dimensional exponential covariance case.

Suggested Citation

  • Joseph Guinness, 2022. "Inverses of Matérn covariances on grids [Spatial modeling with R-INLA: A review]," Biometrika, Biometrika Trust, vol. 109(2), pages 535-541.
    • Handle: RePEc:oup:biomet:v:109:y:2022:i:2:p:535-541.
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    File URL: http://hdl.handle.net/10.1093/biomet/asab017
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    References listed on IDEAS

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    1. Peter Guttorp & Tilmann Gneiting, 2006. "Studies in the history of probability and statistics XLIX On the Matern correlation family," Biometrika, Biometrika Trust, vol. 93(4), pages 989-995, December.
    2. Finn Lindgren & Håvard Rue & Johan Lindström, 2011. "An explicit link between Gaussian fields and Gaussian Markov random fields: the stochastic partial differential equation approach," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 73(4), pages 423-498, September.
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