Bayesian POT modeling for historical data

Journal of Hydrology

Volumn 274, Issue 1-4, 2003, Pages 95-108

  Parent, Eric ^a   Bernier, Jacques ^a  

^a AGROPARISTECH   (France)

Author keywords

Bayesian models; Data augmentation; Extreme value theory; Flood design; Gibbs sampling; Historical information; Markov Chain Monte Carlo methods; Semi conjugate prior

Indexed keywords

ALGORITHMS; CIVIL ENGINEERING; DATA REDUCTION; DECISION MAKING; EXTRAPOLATION; FLOODS; HYDRAULIC STRUCTURES; PROBABILITY;

BAYESIAN MODELING;

HYDROLOGY;

BAYESIAN ANALYSIS; DESIGN FLOOD; EXTREME EVENT; HISTORICAL RECORD;

FRANCE; GARONNE RIVER;

EID: 0037376573     PISSN: 00221694     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0022-1694(02)00396-7     Document Type: Article

References (35)

1. Berger, J.O., 1985. Statistical Decision Theory and Bayesian Analysis, Springer, New York.
2. Berger, J.O., 1999. Bayesian analysis: a look at today and thoughts of tomorrow. ISDS discussion paper 99-30 (available at http://www.stat.duke.edu).
3. Bernardo, J.M., Smith, A.F.M., 1994. Bayesian Theory, Wiley, Londres.
4. Bernier, J., 1967. Les méthodes Bayésiennes en hydrologie. International Hydrology Symposium, Fort Collins, USA.
5. Bernier, J., Parent, E., 2002. Encoding prior knowledge to improve risk analysis of extreme hydrological events via POT modeling, submitted for publication.
6. Box, G., Tiao, G., 1973. Bayesian Inference in Statistical Analysis, Addison-Wesley, reading, MA.
7. Coles, S.G., 2001. An Introduction to Statistical Modeling of Extreme Values, Springer, New York.
8. Coles, S.G., Powell, E.A., 1996. Bayesian methods in extreme value modelling: a review and new developments. Int. Statist. Rev. 64, 119-136.
9. Coles, S.G., Tawn, J.A., 1996. A Bayesian analysis of extreme rainfall data. Appl. Statist. 45 (4), 463-478.
10. Davison, A.C., Smith, R.L., 1990. Models for exceedances over high thresholds (with discussion). J. R. Stat. Soc., B 52, 393-442.
11. Gelfand, A., Smith, A.F.M., 1990. Sampling-based approaches to calculating marginal densities. J. Am. Stat. Assoc. 85, 398-409.
12. Gelman, A., Carlin, J.B., Stern, H.S., Rubin, D.B., 1995. Bayesian Data Analysis, Chapman & Hall, Londres.
13. Hosking, J.R.M., 1985. Maximum likelihood estimation of the parameters of the generalized extreme value distribution. Appl. Stat. 34, 301-310.
14. Hyfran, 2000. Hydrological Frequency Analysis Software package. Chaire d'hydrologie statistique INRS Eau, software (available at http://www.inrs-eau.uquebec.ca/activites/groupes/chaire_hydrol).
15. Kuczera, G., 1999. Comprehensive at-site flood frequency analysis using Monte Carlo Bayesian inference. Water Resour. Res. 35 (5), 1551-1557.
16. Kuczera, G., Parent, E., 1998. Monte Carlo assessment of parameter uncertainty in conceptual catchment models: the Metropolis algorithm. J. Hydrol. 211, 69-85.
17. Martins, E.S., Clarke, R.T., 1993. Likelihood-based confidence intervals for estimating floods with given return periods. J. Hydrol. 147, 61-81.
18. Martins, E.S., Stedinger, J.R., 2001. Generalized maximum likelihood Pareto-Poisson estimators for partial duration series. Water Resour. Res. 37 (10), 2551-2558.
19. Martins, E.S., Stedinger, J.R., 2001. Historical information in a generalized maximum likelihood framework with partial duration and annual maximum series. Water Resour. Res. 37 (10), 2559-2568.
20. Miquel, J., 1984. Guide pratique d'estimation des probabilités de crues, Eyrolles, Paris.
21. NERC, 1975. Flood study report. National Environment Research Council, London.
22. Ouarda, T.B.M., Rasmussen, P.F., Bobée, B., Bernier, J., 1998. Utilisation de l'information historique en analyse hydrologique frequentielle. Rev. Sciences de l'Eau, no special, 41-49.
23. Pardé, M., 1935. Le régime de la Garonne. Revue Géographique des Pyrénées et Sud-Ouest.
24. Pickands, J., 1975. Statistical inference using extreme order statistics. Ann. Stat. 3, 11-130.
25. Raiffa, H., Schlaifer, R., 1961. Applied Statistical Decision Theory, Harvard University Press, Cambridge, MA.
26. Rasmussen, P.F., Ashkar, F., Rosbjerg, D., Bobée, B., 1994. The POT method for flood estimation: a review. In: Hipel, Kluwer (Eds.), Stoch. Stat. Methods Hydrol Envir. Engng, Kluwer, Dordrecht.
27. Robert, C.P., Casella, G., 1998. Monte Carlo Statistical Methods, Springer, Berlin.
28. Smith, R.L., 1985. Maximum Likelihood estimation in a class of nonregular cases. Biometrica 72, 67-90.
29. Smith, R.L., 1986. Extreme value theory based on the r largest annual events.J. Hydrol. 86, 27-43.
30. Spiegelhalter, D.J., Thomas, A., Best, N.G., 1996. Computation on Bayesian graphical models. In: Bernardo, J.M., Berger, J.O., Dawid, A.P., Smith, A.F.M. (Eds.), Bayesian Statistics 5, Oxford University Press, Oxford, pp. 407-425.
31. Stedinger, J.R., Cohn, T.A., 1986. Flood frequency analysis with historical and paleoflood information. Water Resour. Res. 22 (5), 785-793.
32. Tanner, M.A., 1996. Tools for Statistical Inference: Methods for the Exploration of Posterior Distribution and Likelihood Functions, Springer, New York.
33. Tribus, M., 1972. Décision rationnelle dans l'incertain, Masson, Paris.
34. USWRC, 1992. Guidelines for determining flood frequency. US Water Resources Council, Bulletin, vol. 17.B. Hydrology Subcommittee, Office for Water Data Coordination, Washington, DC.
35. Wang, Q.J., 1991. The POT model described by the generalized Pareto distribution with Poisson arrival rate. J. Hydrol. 129, 263-280.