Bayesian model averaging for multivariate extremes
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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.
KeywordsBayesian model averaging Multivariate extremes Parametric modelling Spectral measure
AMS 2000 Subject Classifications62F07 62F15 62H20 62H05 62P12
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- Ballani, F., Schlather, M.: A construction principle for multivariate extreme value distributions. Biometrika 98(3) (2011)Google Scholar
- Cowles, M., Carlin, B.: Markov chain monte carlo convergence diagnostics: a comparative review. J. Am. Stat. Assoc., 883–904 (1996)Google Scholar
- Geweke, J.: Evaluating the accuracy of sampling-based approaches to the calculation of posterior moments. In: In Bayesian Statistics, pp. 169–193. University Press (1992)Google Scholar
- de Haan, L.: Extreme Value Theory, an Introduction, Ferreira, A. Springer Series in Operations Research and Financial Engineering (2006)Google Scholar
- Kass, R., Tierney, L., Kadane, J.: The validity of posterior expansions based on Laplace’s method. Bayesian and Likelihood methods in Statistics and Econometrics 7, 473–488 (1990)Google Scholar
- Resnick, S.: Extreme Values, Regular Variation, and Point Processes, Volume 4 of Applied Probability. A Series of the Applied Probability Trust. Springer-Verlag, New York (1987)Google Scholar
- Resnick, S., Heavy-Tail Phenomena: Probabilistic and Statistical Modeling. Springer Series in Operations Research and Financial Engineering (2007)Google Scholar
- Robert, C.: The Bayesian Choice: from Decision-theoretic Foundations to Computational Implementation. Springer Verlag, New York (2007)Google Scholar
- van der Vaart, A.: Asymptotic Statistics (Cambridge Series in Statistical and Probabilistic Mathematics). Cambridge University Press, Cambridge, MA (2000)Google Scholar