Une procédure bayésienne de sélection/validation différentielle pour déterminer le domaine d'attraction des valeurs extrêmes
Parent, Eric ; Bernier, Jacques
Revue de Statistique Appliquée, Tome 52 (2004), p. 5-31 / Harvested from Numdam
Publié le : 2004-01-01
@article{RSA_2004__52_4_5_0,
     author = {Parent, \'Eric and Bernier, Jacques},
     title = {Une proc\'edure bay\'esienne de s\'election/validation diff\'erentielle pour d\'eterminer le domaine d'attraction des valeurs extr\^emes},
     journal = {Revue de Statistique Appliqu\'ee},
     volume = {52},
     year = {2004},
     pages = {5-31},
     language = {fr},
     url = {http://dml.mathdoc.fr/item/RSA_2004__52_4_5_0}
}
Parent, Eric; Bernier, Jacques. Une procédure bayésienne de sélection/validation différentielle pour déterminer le domaine d'attraction des valeurs extrêmes. Revue de Statistique Appliquée, Tome 52 (2004) pp. 5-31. http://gdmltest.u-ga.fr/item/RSA_2004__52_4_5_0/

Ancey C. (1996), Guide Neige et Avalanche : Connaissances, pratiques, sécurité. Éditions Édisud.

Berger J.O. (1985), Statistical decision theory and Bayesian analysis. Springer Verlag, New York. | MR 804611 | Zbl 0572.62008

Berger J.O. and Pericchi L. (1996), The intrinsic Bayes factor for model selection and prediction. Journal of the American Statistical Association, 91, 109 -122. | MR 1394065 | Zbl 0870.62021

Bernardo J.M. and Smith A.F.M. (1994), Bayesian theory. John Wiley and Sons, Londres. | MR 1274699 | Zbl 0796.62002

Bernier J., Parent E., Boreux J.J. (2000), Statistique pour l'environnement. Traitement bayésien de l'incertitude. Lavoisier, Tec § Doc.

Carlin B.P. and Chib S. (1995), B ayesian Model Choice via Markov Chain Monte Carlo Methods. Journal of the Royal Statistical Society, B 57, 3 473-484. | Zbl 0827.62027

Chaouche A. and Bacro J.N. (2003), A statistical test procedure for the shape parameter of the generalized Pareto distribution, Comp. Stat. Data An. | Zbl pre05373982

Chib S. and Jeliazkov I. (1995), Marginal Likelihood from the Gibbs Output, J. Amer. Stat. Assoc.,90, 1313-1321. | MR 1379473 | Zbl 0868.62027

Chib S. and Jeliazkov I. (2001), Marginal Likelihood from the Metropolis-Hastings Output, J. Amer. Stat. Assoc., 96, 270-281. | MR 1952737 | Zbl 1015.62020

Coles S.G. (2001), An introduction to statistical modeling of extreme values. Springer Verlag, New York. | MR 1932132 | Zbl 0980.62043

Coles S.G. and Powell E.A. (1996), Bayesian methods in extreme value modelling : a review and new developments. Internat. Stat. Rev. 64, 119- 136. | Zbl 0853.62025

Davison A.C. and Smith R.L. (1990), Models for exceedances over high thresholds (with discussion). Journal of the Royal Statistical Society, B 52, 393-442. | MR 1086795 | Zbl 0706.62039

Ferguson T. (1973), A Bayesian Analysis of Some Non Parametric Problems. Annals Statist. 1, 209-230. | MR 350949 | Zbl 0255.62037

Fisher R.A., Tippett L.H.C. (1928), Limiting forms of the frequency distribution of the largest or the smallest member of a sample. Proc. Cambridge Philo Soc. 24, 180-190. | JFM 54.0560.05

Fortin V., Bernier J. et Bobée B. (1997), Simulation, Bayes, and bootstrap in statistical hydrology. Water Resour. Res., 33 (3) : 439-448.

Fréchet M. (1927), Sur la loi de probabilité de l'écart maximum. Annals of Polnish Math. Soc. 6, 93. | JFM 54.0562.06

Gelfand A.E. and Dey D.K. (1995), Bayesian Model Choice : Asymptotics and exact calculations. Journal of the Royal Statistical Society, B 56, 3 501-514. | MR 1278223 | Zbl 0800.62170

Gelfand A. and Smith A.F.M. (1990), Sampling-based approaches to calculating marginal densities. Journ. Amer. Stat. Ass., 85: 398-409. | MR 1141740 | Zbl 0702.62020

Gelman A., Carlin J.B., Stern H.S. and Rubin D.B. (1995), Bayesian data analysis. Chapman and Hall, Londres. | MR 1385925 | Zbl 0914.62018

Gelman A. and Rubin D.B. (1992), Inference from iterative simulation using multiple sequences, Statistical Science, 7, 457-511.

Gelman A., Meng X. and Stern H. (1996), Posterior Predictive Assessment of Model Fitness via Realized Discrepancies. Statistica Sinica 6, 733- 807 | MR 1422404 | Zbl 0859.62028

Han C. and Carlin B.P. (2000), MCMC methods for computing Bayes factors : a comparative review. Division of Biostatistics, University of Minnesota. MCMCpreprint, available at http ://www.stat.duke.edu.

Hoeting J.A., Madigan D., Raftery A.E., Volinsky C.T. (1999), Bayesian model averaging : A Tutorial, Statistical Science, 14, 4, p. 382- 417. | MR 1765176 | Zbl 1059.62525

Kadane J.B., Wolson L.J., O'Hagan A., Craig R. (1998), Papers on 'Elicitation' and Discussions. The Statistician 47 (1), 3-53.

Kass R.E. and Raftery A.E. (1994), Bayes factors. J. Amer. Stat. Assoc., 90, 773-795. | Zbl 0846.62028

Laplace P.S. (1847), Œuvres, Tome VII, Théorie analytique des probabilités. Reprint 1995. Editions Jacques Gabay, Paris.

Lehman E.L. (1986), Theory ofpoint estimation. 2nd edition. John Wiley and Sons, New York.

O'Hagan A. (1997), Properties of intrinsic and fractional Bayes factors. Test 6, 101-118. | MR 1466435 | Zbl 0891.62001

O'Hagan A. (1998), Elicitation expert beliefs in substancial practical applications - The Statistician 47 (1), 21- 35.

Parent E., Bernier J. (2001), Méthodes bayésiennes et modélisation des risques géophysiques extrêmes. La Revue de Modulad. 28: 1- 26. INRIA.

Parent E., Bernier J. (2002), Bayesian P.O.T. modeling for historical data. Journal of Hydrology, 274: 95-108.

Pickands J. (1975), Statistical inference using extreme order statistics. Ann. Stat., 3, 11-130. | MR 423667 | Zbl 0312.62038

Smith R.L. (1984), Threshold model for sample extreme in T. de Oliveira (ed.), Statistical Extremes and Applications, 621- 638. Reidel Dordrecht. | MR 784846 | Zbl 0574.62090

Tanner M.A. (1996), Tools for statistical inference : methods for the exploration of posterior distribution and likelihoodfunctions. Springer Verlag, New York. | MR 1396311 | Zbl 0846.62001