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Conditional simulation of max-stable processes

Author

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  • C. Dombry
  • F. Éyi-Minko
  • M. Ribatet

Abstract

Since many environmental processes are spatial in extent, a single extreme event may affect several locations, and the spatial dependence must be taken into account in an appropriate way. This paper proposes a framework for conditional simulation of max-stable processes and gives closed forms for the regular conditional distributions of Brown--Resnick and Schlather processes. We test the method on simulated data and present applications to extreme rainfall around Zurich and extreme temperatures in Switzerland. The proposed framework provides accurate conditional simulations and can handle problems of realistic size. Copyright 2013, Oxford University Press.

Suggested Citation

  • C. Dombry & F. Éyi-Minko & M. Ribatet, 2013. "Conditional simulation of max-stable processes," Biometrika, Biometrika Trust, vol. 100(1), pages 111-124.
    • Handle: RePEc:oup:biomet:v:100:y:2013:i:1:p:111-124
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    File URL: http://hdl.handle.net/10.1093/biomet/ass067
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    Cited by:

    1. Koch, Erwan & Robert, Christian Y., 2022. "Stochastic derivative estimation for max-stable random fields," European Journal of Operational Research, Elsevier, vol. 302(2), pages 575-588.
    2. Hashorva, Enkelejd, 2018. "Representations of max-stable processes via exponential tilting," Stochastic Processes and their Applications, Elsevier, vol. 128(9), pages 2952-2978.
    3. Oesting, Marco, 2015. "On the distribution of a max-stable process conditional on max-linear functionals," Statistics & Probability Letters, Elsevier, vol. 100(C), pages 158-163.
    4. Hentschel, Manuel & Engelke, Sebastian & Segers, Johan, 2022. "Statistical Inference for Hüsler–Reiss Graphical Models Through Matrix Completions," LIDAM Discussion Papers ISBA 2022032, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    5. Opitz, T., 2013. "Extremal t processes: Elliptical domain of attraction and a spectral representation," Journal of Multivariate Analysis, Elsevier, vol. 122(C), pages 409-413.

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