An application of Bayesian analysis and Markov chain Monte Carlo methods to the estimation of a regional trend in annual maxima

Water Resources Research

Volumn 42, Issue 12, 2006, Pages

  Renard, B ^a   Garreta, V ^a   Lang, M ^a  

^a CENTRE DE LYON VILLEURBANNE   (France)

Author keywords

[No Author keywords available]

Indexed keywords

DISCHARGE (FLUID MECHANICS); MARKOV PROCESSES; MATHEMATICAL MODELS; MONTE CARLO METHODS;

ANNUAL MAXIMA; BAYESIAN ANALYSIS; COMPLEX MODELS;

HYDROLOGY;

DISCHARGE (FLUID MECHANICS); HYDROLOGY; MARKOV PROCESSES; MATHEMATICAL MODELS; MONTE CARLO METHODS;

BAYESIAN ANALYSIS; DISCHARGE; FREQUENCY ANALYSIS; HYDROLOGY; MARKOV CHAIN; MONTE CARLO ANALYSIS;

EID: 33845536869     PISSN: 00431397     EISSN: None     Source Type: Journal    
DOI: 10.1029/2005WR004591     Document Type: Article

References (65)

1. Bernier, J. (1994), Statistical detection of changes in geophysical series, Eng. Risk Nat. Resour. Manage., 275, 159-176.
2. Bortot, P., S. Coles, and J. A. Tawn (2000), The multivariate Gaussian tail model: An application to oceanographic data, Appl. Stat., 49, 31-49.
3. Buishand, T. A. (1991), Extreme rainfall estimation by combining data from several sites, Hydrol. Sci. J., 36, 345-365.
4. Chib, S. (1995), Marginal likelihood from the Gibbs output, J. Am. Stat. Assoc., 90, 1313-1321.
5. Coles, S. (2001), An Introduction to Statistical Modeling of Extreme Values, 210 pp., Springer, New York.
6. Coles, S., and L. Pericchi (2003), Anticipating catastrophes through extreme value modelling, J. R. Stat. Soc., Ser. C, 52, 405-416.
7. Coles, S., and J. A. Tawn (1990), Statistics of coastal flood prevention, Philos. Trans. R. Soc. London, Ser. A, 332, 457-476.
8. Coles, S. G., and J. A. Tawn (1996), A Bayesian analysis of extreme rainfall data, J. R. Stat. Soc., Ser. C, 45, 463-478.
9. Coles, S., L. R. Pericchi, and S. Sisson (2003), A fully probabilistic approach to extreme rainfall modelling, J. Hydrol., 273, 35-50.
10. Cooley, D. (2005), Statistical Analysis of Extremes Motivated by Weather and Climate Studies: Applied and Theoretical Advances, 122 pp., Univ. of Colo., Boulder.
11. Dalrymple, T. (1960), Flood frequency analyses, U.S. Geol. Surv. Water Supply Pap., 1553-A.
12. De Haan, L., and T. T. Pereira (2006), Spatial extremes: Models for the stationary case, Ann. Stat., 34, 146-168.
13. El Adlouni, S., A. C. Favre, and B. Bobee (2006), Comparison of methodologies to assess the convergence of Markov chain Monte Carlo methods, Comput. Stat. Data Anal., 50, 2685-2701.
14. Favre, A.-C., S. El Adlouni, L. Perreault, N. Thiémonge, and B. Bobée (2004), Multivariate hydrological frequency analysis using copulas, Water Resour. Res., 40, W01101, doi:10.1029/2003WR002456.
15. Fisher, R. A., and L. H. Tippelt (1928), Limiting forms of the frequency distribution of the largest or smallest member of a sample, Proc. Cambridge Philos. Soc., 24, 180-190.
16. Gelfand, A. E., and A. F. M. Smith (1990), Sampling-based approaches to calculating marginal densities, J. Am. Stat. Assoc., 85, 398-409.
17. Gelman, A., J. B. Carlin, H. S. Stern, and D. B. Rubin (1995), Bayesian Data Analysis, edited by C. Hall, 526 pp., CRC, Boca Raton, Fla.
18. Gelman, A., G. O. Roberts, and W. R. Gilks (1996), Efficient metropolis jumping rules, in Bayesian Statistics, vol. 5, pp. 599-607, Oxford Univ. Press, New York.
19. Geman, S., and D. Geman (1984), Stochastic relaxation, Gibbs distributions, and the Bayesian restoration of images, IEEE Trans. Pattern Anal. Mach. Intel., 6, 721-741.
20. Gilks, W. R., and P. Wild (1992), Adaptive rejection sampling for Gibbs sampling, J. R. Stat. Soc., Ser. C, 41, 337-348.
21. Gilks, W. R., N. G. Best, and K. K. C. Tan (1995), Adaptive rejection metropolis sampling within Gibbs sampling, J. R. Stat. Soc., Ser. C, 44, 455-472.
22. Haario, H., E. Saksman, and J. Tamminen (2001), An adaptive Metropolis algorithm, Bernoulli, 7, 223-242.
23. Haario, H., E. Saksman, and J. Tamminen (2005), Componentwise adaptation for high dimensional MCMC, Comput. Stat., 20, 265-273.
24. Hastings, W. K. (1970), Monte Carlo sampling methods using Markov chains and their applications, Biometrika, 57, 97-109.
25. Hoeting, J. A., D. Madigan, A. E. Raftery, and C. T. Volinsky (1999), Bayesian model averaging: A tutorial, Stat. Sci., 14, 382-401.
26. Hosking, J. R. M., and J. R. Wallis (1988), The effect of intersite dependence on regional flood frequency analysis, Water Resour. Res., 24, 588-600.
27. Hosking, J. R. M., and J. R. Wallis (1997), Regional Frequency Analysis: An Approach Based on L-Moments, 226 pp., Cambridge Univ. Press, New York.
28. Jenkihson, A. F. (1955), The frequency distribution of the annual maximum (or minimum) values of meteorological elements, Q. J. R. Meteorol. Soc., 81, 158-171.
29. Kass, R. E., and A. E. Raftery (1995), Bayes factors, J. Am. Stat. Assoc., 90, 773-795.
30. Katz, R. W., M. B. Parlange, and P. Naveau (2002), Statistics of extremes in hydrology, Adv. Water Resour., 25, 1287-1304.
31. Khodja, H., H. Lubès-Niel, J. M. Sabatier, E. Servat, and J. E. Paturel (1998), Analyse spatio-temporelle de données pluviomé triques en Afrique de l'Ouest, Recherche d'une rupture en moyenne, Une alternative intéressante: Les tests de permutations, Rev. Stat. Appl., 46, 95-110.
32. Lee, A. F. S., and S. M. Heghinian (1977), A shift of the mean level in a sequence of independent normal random variables-A Bayesian approach, Technometrics, 19, 503-506.
33. Lu, Z. Q., and L. M. Berliner (1999), Markov switching time series models with application to a daily runoff series, Water Resour. Res., 35, 523-534.
34. Madsen, H., and D. Rosbjerg (1997), The partial duration series method in regional index-flood modeling, Water Resour. Res., 33, 737-746.
35. Marshall, L., D. Nott, and A. Sharma (2004), A comparative study of Markov chain Monte Carlo methods for conceptual rainfall-runoff modeling, Water Resour. Res., 40, W02501, doi:10.1029/2003WR002378.
36. Martins, E. S., and J. R. Stedinger (2000), Generalized maximum-likelihood generalized extreme-value quantile estimators for hydrologic data, Water Resour. Res., 36, 737-744.
37. Metropolis, N., and S. Ulam (1949), The Monte Carlo method, J. Am. Stat. Assoc., 44, 335-341.
38. Metropolis, N., A. W. Rosenbluth, M. N. Rosenbluth, A. H. Teller, and E. Teller (1953), Equation of state calculations by fast computing machines, J. Chem. Phys., 21, 1087-1092.
39. Moyeed, R. A., and R. T. Clarice (2005), The use of Bayesian methods for fitting rating curves, with case studies, Adv. Water Resour., 28, 807-818.
40. Naveau, P., D. Cooley, and P. Poneet (2005), Spatial extremes analysis in climate studies, paper presented at 4th Conference on Extreme Value Analysis: Probabilistic and Statistical Models and Their Applications, Dan. Res. Network for Math. Phys. and Stochastics, Gothenburg, Sweden.
41. Ouarda, T. B. M. J., M. Lang, B. Bobee, J. Bernier, and P. Bois (1999), Analysis of regional flood models utilized in France and Quebec, Rev. Sci. Eau, 12, 155-182.
42. Parent, E., and J. Bernier (2003), Encoding prior experts judgments to improve risk analysis of extreme hydrological events via POT modelling, J. Hydrol., 283, 1-18.
43. Perreault, L. (2000), Analyse bayésienne rétrospective d'une rupture dans les séquences de variables aléatoires hydrologiques, thesis, 200 pp., Ecole Natl. du Génie Rural et des Eaux et Forêts, Paris.
44. Perreault, L., and V. Fortin (2003), Mixture and hidden Markov models for peak flow analysis, paper presented at Seizièmes Entretiens, Cent. Jacques Cartier, Lyon, France.
45. Perteault, L., M. Hache, M. Slivitzky, and B. Bobee (1999), Detection of changes in precipitation and runoff over eastern Canada and US using a Bayesian approach, Stochastic Environ. Res. Risk Assess., 13, 201-216.
46. Perreault, L., J. Bernier, B. Bobee, and E. Parent (2000a), Bayesian change-point analysis in hydrometeorological time series, part 1. The normal model revisited, J. Hydrol., 235, 221-241.
47. Perreault, L., J. Bernier, B. Bobee, and E. Parent (2000b), Bayesian change-point analysis in hydrometeorological time series, part 2. Comparison of change-point models and forecasting, J. Hydrol., 235, 242-263.
48. Perreault, L., E. Parent, J. Bernier, B. Bobee, and M. Slivitzky (2000c), Retrospective multivariate Bayesian change-point analysis: A simultaneous single change in the mean of several hydrological sequences, Stochastic Environ. Res. Risk Assess., 14, 243-261.
49. Reis, D. S., and J. R. Stedinger (2005), Bayesian MCMC flood frequency analysis with historical information, J. Hydrol., 313, 97-116.
50. Renard, B., M. Lang, and P. Bois (2006), Statistical analysis of extreme events in a non-stationary context via a Bayesian framework, Stochastic Environ. Res. Risk Assess., doi:10.1007/s00477-006-0047-4, in press.
51. Ribatet, M., E. Sauquet, J. M. Gresillon, and T. B. M. J. Ouarda (2006), A regional Bayesian POT model for flood frequency analysis, Stochastic Environ. Res. Risk Assess., doi:10.1007/s00477-006-0068-z, in press.
52. Ritter, C., and M. A. Tanner (1992), Facilitating the Gibbs Sampler-The Gibbs Stopper and the Griddy-Gibbs Sampler, J. Am. Stat. Assoc., 87, 861-868.
53. Roberts, G. O., and W. R. Gilks (1994), Convergence of adaptive direction sampling, J. Multivariate Anal., 49, 287-298.
54. Schalther, M., and J. A. Tawn (2003), A dependence measure for multivariate and spatial extreme values: Properties and inference, Biometrika, 90, 139-156.
55. Stedinger, J. R. (1983), Estimating a regional flood frequency distribution, Water Resour. Res., 19, 503-510.
56. Tanner, M. A. (1996), Tools for Statistical Inference, 208 pp., Springer, New York.
57. Tapsoba, D., M. Hache, L. Perreault, and B. Bobee (2004), Bayesian rainfall variability analysis in West Africa along cross sections in space-time grid boxes, J. Clim., 17, 1069-1082.
58. Thyer, M., and G. Kuczera (2000), Modeling long-term persistence in hydroclimatic time series using a hidden state Markov model, Water Resour. Res., 36, 3301-3310.
59. Thyer, M., and G. Kuczera (2003a), A hidden Markov model for modelling long-term persistence in multi-site rainfall time series. 1. Model calibration using a Bayesian approach, J. Hydrol., 275, 12-26.
60. Thyer, M., and G. Kuczera (2003b), A hidden Markov model for modelling long-term persistence in multi-site rainfall time series. 2. Real data analysis, J. Hydrol., 275, 27-48.
61. Thyer, M., G. Kuczera, and Q. J. Wang (2002), Quantifying parameter uncertainty in stochastic models using the Box-Cox transformation, J. Hydrol., 265, 246-257.
62. Tierney, L. (1994a), Markov-Chains for exploring posterior distributions, Ann. Stat., 22, 1701-1728.
63. Tierney, L. (1994b), Markov-Chains for exploring posterior distributions-Rejoinder, Ann. Stat., 22, 1758-1762.
64. Tierney, L., and A. Mira (1999), Some adaptive Monte Carlo methods for Bayesian inference, Stat. Med., 18, 2507-2515.
65. Wang, Q. J. (2001), A Bayesian joint probability approach for flood record augmentation, Water Resour. Res., 37, 1707-1712.