Bayesian Model Averaging for multivariate extremes

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 etermine if the BMA approach can offer an added value when analyzing extreme values.
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Anne Sabourin, Naveau Philippe, Fougères Anne-Laure. Bayesian Model Averaging for multivariate extremes. Extremes, Springer Verlag (Germany), 2013, 16 (3), pp.325-350. ⟨10.1007/s10687-012-0163-0⟩. ⟨hal-00880779⟩

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