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Spatial Matérn Fields Driven by Non-Gaussian Noise

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  • David Bolin

Abstract

type="main" xml:id="sjos12046-abs-0001"> The article studies non-Gaussian extensions of a recently discovered link between certain Gaussian random fields, expressed as solutions to stochastic partial differential equations (SPDEs), and Gaussian Markov random fields. The focus is on non-Gaussian random fields with Matérn covariance functions, and in particular, we show how the SPDE formulation of a Laplace moving-average model can be used to obtain an efficient simulation method as well as an accurate parameter estimation technique for the model. This should be seen as a demonstration of how these techniques can be used, and generalizations to more general SPDEs are readily available.

Suggested Citation

  • David Bolin, 2014. "Spatial Matérn Fields Driven by Non-Gaussian Noise," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 41(3), pages 557-579, September.
    • Handle: RePEc:bla:scjsta:v:41:y:2014:i:3:p:557-579
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    File URL: http://hdl.handle.net/10.1111/sjos.12046
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    References listed on IDEAS

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    1. Bolin, David & Lindgren, Finn, 2013. "A comparison between Markov approximations and other methods for large spatial data sets," Computational Statistics & Data Analysis, Elsevier, vol. 61(C), pages 7-21.
    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.
    3. Wiktorsson, Magnus, 2002. "Simulation of stochastic integrals with respect to Lévy processes of type G," Stochastic Processes and their Applications, Elsevier, vol. 101(1), pages 113-125, September.
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    Cited by:

    1. Walder, Adam & Hanks, Ephraim M., 2020. "Bayesian analysis of spatial generalized linear mixed models with Laplace moving average random fields," Computational Statistics & Data Analysis, Elsevier, vol. 144(C).
    2. Korte-Stapff, Moritz & Karvonen, Toni & Moulines, Éric, 2025. "Smoothness estimation for Whittle–Matérn processes on closed Riemannian manifolds," Stochastic Processes and their Applications, Elsevier, vol. 189(C).
    3. Jafari Khaledi, Majid & Zareifard, Hamid & Boojari, Hossein, 2023. "A spatial skew-Gaussian process with a specified covariance function," Statistics & Probability Letters, Elsevier, vol. 192(C).
    4. Heinrich, Claudio & Pakkanen, Mikko S. & Veraart, Almut E.D., 2019. "Hybrid simulation scheme for volatility modulated moving average fields," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 166(C), pages 224-244.
    5. Özgür Asar & David Bolin & Peter J. Diggle & Jonas Wallin, 2020. "Linear mixed effects models for non‐Gaussian continuous repeated measurement data," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 69(5), pages 1015-1065, November.
    6. Jonas Wallin & David Bolin, 2015. "Geostatistical Modelling Using Non-Gaussian Matérn Fields," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 42(3), pages 872-890, September.

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