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Geostatistical Modelling Using Non-Gaussian Matérn Fields

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  • Jonas Wallin
  • David Bolin

Abstract

type="main" xml:id="sjos12141-abs-0001"> This work provides a class of non-Gaussian spatial Matérn fields which are useful for analysing geostatistical data. The models are constructed as solutions to stochastic partial differential equations driven by generalized hyperbolic noise and are incorporated in a standard geostatistical setting with irregularly spaced observations, measurement errors and covariates. A maximum likelihood estimation technique based on the Monte Carlo expectation-maximization algorithm is presented, and a Monte Carlo method for spatial prediction is derived. Finally, an application to precipitation data is presented, and the performance of the non-Gaussian models is compared with standard Gaussian and transformed Gaussian models through cross-validation.

Suggested Citation

  • 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.
    • Handle: RePEc:bla:scjsta:v:42:y:2015:i:3:p:872-890
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    File URL: http://hdl.handle.net/10.1111/sjos.12141
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    References listed on IDEAS

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    1. 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.
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    8. David Bolin & Finn Lindgren, 2015. "Excursion and contour uncertainty regions for latent Gaussian models," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 77(1), pages 85-106, January.
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    2. Caamaño-Carrillo, Christian & Bevilacqua, Moreno & López, Cristian & Morales-Oñate, Víctor, 2024. "Nearest neighbors weighted composite likelihood based on pairs for (non-)Gaussian massive spatial data with an application to Tukey-hh random fields estimation," Computational Statistics & Data Analysis, Elsevier, vol. 191(C).
    3. 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).
    4. Klein, Nadja & Herwartz, Helmut & Kneib, Thomas, 2020. "Modelling regional patterns of inefficiency: A Bayesian approach to geoadditive panel stochastic frontier analysis with an application to cereal production in England and Wales," Journal of Econometrics, Elsevier, vol. 214(2), pages 513-539.
    5. Ganggang Xu & Marc G. Genton, 2017. "Tukey -and- Random Fields," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 112(519), pages 1236-1249, July.
    6. 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.

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