Bayesian model averaging for multivariate extremes

Extremes volume 16, pages325–350(2013)Cite this article

Abstract

The main framework of multivariate extreme value theory is well-known in terms of probability, but inference and model choice remain an active research field. Theoretically, an angular measure on the positive quadrant of the unit sphere can describe the dependence among very high values, but no parametric form can entirely capture it. The practitioner often makes an assertive choice and arbitrarily fits a specific parametric angular measure on the data. Another statistician could come up with another model and a completely different estimate. This leads to the problem of how to merge the two different fitted angular measures. One natural way around this issue is to weigh them according to the marginal model likelihoods. This strategy, the so-called Bayesian Model Averaging (BMA), has been extensively studied in various context, but (to our knowledge) it has never been adapted to angular measures. The main goal of this article is to determine if the BMA approach can offer an added value when analyzing extreme values.

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Affiliations

  1. Université de Lyon, CNRS UMR 5208, Université Lyon 1, Institut Camille Jordan, 43 blvd. du 11 novembre 1918, 69622, Villeurbanne cedex, France

    Anne Sabourin & Anne-Laure Fougères

  2. Laboratoire des Sciences du Climat et de l’Environnement, CNRS-CEA-UVSQ, 91191, Gif-sur-Yvette, France

    Anne Sabourin & Philippe Naveau

Authors
  1. Anne Sabourin
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  2. Philippe Naveau
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  3. Anne-Laure Fougères
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Correspondence to Anne Sabourin.

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Sabourin, A., Naveau, P. & Fougères, A. Bayesian model averaging for multivariate extremes. Extremes 16, 325–350 (2013). https://doi.org/10.1007/s10687-012-0163-0

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Keywords

  • Bayesian model averaging
  • Multivariate extremes
  • Parametric modelling
  • Spectral measure

AMS 2000 Subject Classifications

  • 62F07
  • 62F15
  • 62H20
  • 62H05
  • 62P12