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High resolution simulation of nonstationary Gaussian random fields

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  • Kleiber, William

Abstract

Simulation of random fields is a fundamental requirement for many spatial analyses. For small spatial networks, simulations can be produced using direct manipulations of the covariance matrix. Larger high resolution simulations are most easily available for stationary processes, where algorithms such as circulant embedding can be used to simulate a process at millions of locations. We discuss an approach to simulating high resolution nonstationary Gaussian processes that relies on generating a stationary random field followed by a nonlinear deformation to produce a nonstationary field. A spatially varying variance coefficient accounts for local scale effects. The nonstationary covariance function is estimated nonparametrically, and the deformation function is then estimated in a variational framework. We illustrate the proposed approach on synthetic datasets, a challenging temperature dataset over the state of Colorado and a regional climate model over North America.

Suggested Citation

  • Kleiber, William, 2016. "High resolution simulation of nonstationary Gaussian random fields," Computational Statistics & Data Analysis, Elsevier, vol. 101(C), pages 277-288.
  • Handle: RePEc:eee:csdana:v:101:y:2016:i:c:p:277-288
    DOI: 10.1016/j.csda.2016.03.005
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    References listed on IDEAS

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    6. Kleiber, William & Nychka, Douglas, 2012. "Nonstationary modeling for multivariate spatial processes," Journal of Multivariate Analysis, Elsevier, vol. 112(C), pages 76-91.
    7. 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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    Cited by:

    1. Monbet, Valérie & Ailliot, Pierre, 2017. "Sparse vector Markov switching autoregressive models. Application to multivariate time series of temperature," Computational Statistics & Data Analysis, Elsevier, vol. 108(C), pages 40-51.
    2. Gangloff, Hugo & Courbot, Jean-Baptiste & Monfrini, Emmanuel & Collet, Christophe, 2021. "Unsupervised image segmentation with Gaussian Pairwise Markov Fields," Computational Statistics & Data Analysis, Elsevier, vol. 158(C).

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