Extremes

, Volume 16, Issue 3, pp 325–350

Bayesian model averaging for multivariate extremes

Authors

    • Université de Lyon, CNRS UMR 5208, Université Lyon 1Institut Camille Jordan
    • Laboratoire des Sciences du Climat et de l’EnvironnementCNRS-CEA-UVSQ
  • Philippe Naveau
    • Laboratoire des Sciences du Climat et de l’EnvironnementCNRS-CEA-UVSQ
  • Anne-Laure Fougères
    • Université de Lyon, CNRS UMR 5208, Université Lyon 1Institut Camille Jordan
Article

DOI: 10.1007/s10687-012-0163-0

Cite this article as:
Sabourin, A., Naveau, P. & Fougères, A. Extremes (2013) 16: 325. doi:10.1007/s10687-012-0163-0

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.

Keywords

Bayesian model averaging Multivariate extremes Parametric modelling Spectral measure

AMS 2000 Subject Classifications

62F07 62F15 62H20 62H05 62P12

Copyright information

© Springer Science+Business Media New York 2013