Bayesian nonstationary frequency analysis of hydrological variables

Journal of the American Water Resources Association

Volumn 47, Issue 3, 2011, Pages 496-505

  Ouarda, T B M J ^a,b   El Adlouni, S ^c  

^a KHALIFA UNIVERSITY   (United Arab Emirates)

^b CENTRE EAU TERRE ENVIRONNEMENT   (Canada)

^c INSEA   (Morocco)

Author keywords

Frequency analysis; Generalized maximum likelihood; Hydrological variable; Maximum likelihood; Nonstationary model; Parameter estimation; Quantile; Reversible jump Monte Carlo Markov Chain

Indexed keywords

FREQUENCY ANALYSIS; GENERALIZED MAXIMUM LIKELIHOOD; HYDROLOGICAL VARIABLES; NONSTATIONARY MODEL; QUANTILE; REVERSIBLE JUMP;

BAYESIAN NETWORKS; ESTIMATION; FREQUENCY ESTIMATION; MARKOV PROCESSES; MONTE CARLO METHODS;

MAXIMUM LIKELIHOOD ESTIMATION;

BAYESIAN ANALYSIS; COVARIANCE ANALYSIS; FREQUENCY ANALYSIS; HYDROLOGICAL MODELING; MAXIMUM LIKELIHOOD ANALYSIS; MONTE CARLO ANALYSIS;

EID: 79957939654     PISSN: 1093474X     EISSN: 17521688     Source Type: Journal    
DOI: 10.1111/j.1752-1688.2011.00544.x     Document Type: Article

References (53)

1. Akaike, H., 1974. A New Look at the Statistical Model Identification. IEEE Transactions of Automatic Control AC-19(16):716-722.
2. Beaulieu, C., O. Seidou, T.B.M.J. Ouarda, and X. Zhang, 2009. Intercomparison of Homogenization Techniques for Precipitation Data Continued: Comparison of Two Recent Bayesian Change Point Models. Water Resources Research 45:W08410, doi.
3. Beguería, S., M. Angulo-Martínez, S.M. Vicente-Serrano, J.I. López-Moreno, and A. El-Kenawy, 2010. Assessing Trends in Extreme Precipitation Events Intensity and Magnitude Using Non-Stationary Peaks-Over-Threshold Analysis: A Case Study in Northeast Spain From 1930 to 2006. International Journal of Climatology 31(4):619-632, doi.
4. Berger, J.O., 1985. Statistical Decision Theory and Bayesian Analysis. Springer-Verlag, New York.
5. Cannon, A.J., 2010. A Flexible Nonlinear Modeling Framework for Nonstationary Generalized Extreme Value Analysis in Hydroclimatology. Hydrological Processes 24:673-685, doi.
6. Cohn, T.A. and H.F. Lins, 2005. Nature's Style: Naturally Trendy. Geophysical Research Letters 32, L23402:1-5, doi.
7. Coles, G.S., 2001. An Introduction to Statistical Modeling of Extreme Values. Springer, London, 208 pp.
8. Cunderlik, J.M., V. Jourdain, T.B.M.J. Ouarda, and B. Bobée, 2007. Local Non-Stationary Flood-Duration-Frequency Modeling. Canadian Water Resources Journal 32(1):43-58.
9. Cunderlik, J.M. and T.B.M.J. Ouarda, 2006. Regional Flood-Duration-Frequency Modeling in a Changing Environment. Journal of Hydrology 318:276-291, doi.
10. Davis, D., C.C. Kisiel, and L. Duckstein, 1972. Bayesian Decision Theory Applied to Design in Hydrology. Water Resources Research 8:33-41.
11. Draper, D., 1995. Assessment and Propagation of Model Uncertainty. Journal of the Royal Statistical Society. Series B (Methodological) 57:45-97.
12. El-Adlouni, S., A.C. Favre, and B. Bobée, 2006. Comparison of Methodologies to Assess the Convergence of Markov Chain Monte Carlo Methods. Computational Statistics and Data Analysis 50(10):2685-2701.
13. El-Adlouni, S. and T.B.M.J. Ouarda, 2008. Comparison of Methods for Estimating the Parameters of the Non-Stationary GEV Model. Revue des Sciences de l'Eau 21(1): 35-50. ISSN: 1718-8598.
14. El-Adlouni, S. and T.B.M.J. Ouarda, 2009. Joint Bayesian Model Selection and Parameter Estimation of the Generalized Extreme Value Model With Covariates Using Birth-Death Markov Chain Monte Carlo. Water Resources Research 45:W06403, doi.
15. El-Adlouni, S., T.B.M.J. Ouarda, X. Zhang, R. Roy, and B. Bobée, 2007. Generalized Maximum Likelihood Estimators of the Non-Stationary GEV Model Parameters. Water Resources Research 43:W03410, doi.
16. Fisher, R.A., 1929. Moments and Product Moments of Sampling Distributions. Proceedings of the London Mathematical Society 30:199-238.
17. Gilks, W.R., S. Richardson, and D. Spiegelhalter, 1996. Markov Chain Monte Carlo in Practice. CRC Press, Boca Raton, Florida.
18. Green, P.J., 1995. Reversible Jump Markov Chain Monte Carlo Computation and Bayesian Model Determination. Biometrika 82(4):711-732.
19. Green, P.J., 2003. Trans-Dimensional Markov Chain Monte Carlo. In: Highly Structured Stochastic Systems, P.J. Green, N. Lid Hjort, and S. Richardson (Editors). Oxford Statistical Science Series, 27, Oxford University Press.
20. Hamed, K.H. and A.R. Rao, 1998. A Modified Mann-Kendall Trend Test for Autocorrelated Data. Journal of Hydrology 204:219-246.
21. Hastings, W., 1970. Monte Carlo Sampling Methods Using Markov Chains and Their Applications. Biometrika 57:97-109.
22. Hosking, J.R.M., 1990. L-Moments: Analysis and Estimation of Distributions Using Linear Combinations of Order Statistics. Journal of Royal Statistical Society 52:105-124.
23. Huang, N.E. and Z.H. Wu, 2008. A Review on Hilbert-Huang Transform: Method and Its Applications to Geophysical Studies. Reviews of Geophysics, RG2006, 46(2):1-23.
24. Hundecha, Y., A. St-Hilaire, T.B.M.J. Ouarda, S. El-Adlouni, and P. Gachon, 2008. A Non-Stationary Extreme Value Analysis for the Assessment of Changes in Extreme Annual Wind Speed Over the Gulf of St. Lawrence, Canada. Journal of Applied Meteorology and Climatology 47:2745-2759, doi.
25. IPCC (Intergovernmental Panel for Climate Change), 2001. Climate Change 2001: Impacts, Adaptation and Vulnerability. Cambridge University Press, New York.
26. Jenkinson, A.F., 1955. The Frequency Distribution of the Annual Maximum (or Minimum) of Meteorological Elements. Quarterly Journal of the Royal Meteorological Society 81:158-171.
27. Khaliq, M.N., T.B.M.J. Ouarda, and P. Gachon, 2009a. Identification of Temporal Trends in Annual and Seasonal Low Flows Occurring in Canadian Rivers: The Effect of Short- and Long-Term Persistence. Journal of Hydrology 368:183-197, doi.
28. Khaliq, M.N., T.B.M.J. Ouarda, P. Gachon, and B. Bobée, 2006. Frequency Analysis of a Sequence of Dependent and/or Non-Stationary Hydro-Meteorological Observations: A Review. Journal of Hydrology 329:534-552, doi.
29. Khaliq, M.N., T.B.M.J. Ouarda, P. Gachon, L. Sushama, and A. St-Hilaire, 2009b. Identification of Hydrological Trends in the Presence of Serial and Cross Correlations: A Review of Selected Methods and Their Application to Annual Flow Regimes of Canadian Rivers. Journal of Hydrology 368:117-130, doi.
30. Koutsoyiannis, D., 2003. Climate Change, the Hurst Phenomenon, and Hydrological Statistics. Hydrological Sciences Journal 48(1):3-24.
31. Koutsoyiannis, D. and A. Montanari, 2007. Statistical Analysis of Hydroclimatic Time Series: Uncertainty and Insights. Water Resources Research 43(5), W05429:1-9, doi.
32. Krzysztofowicz, R., 1983. Why Should a Forecaster and a Decision Maker Use Bayes Theorem. Water Resources Research 19:327-336.
33. Krzysztofowicz, R., 1999. Bayesian Theory of Probabilistic Forecasting via Deterministic Hydrologic Model. Water Resources Research 35(9):2739-2750.
34. Kuczera, G., 1999. Comprehensive At-Site Flood Frequency Analysis Using Monte Carlo Bayesian Inference. Water Resources Research 34(6):1551-1558.
35. Kwon, H.-H., C. Brown, and U. Lall, 2008. Climate Informed Flood Frequency Analysis and Prediction in Montana Using Hierarchical Bayesian Modeling. Geophysical Research Letters 35:L05404, doi.
36. Leclerc, M. and T.B.M.J. Ouarda, 2007. Non-Stationary Regional Flood Frequency Analysis at Ungauged Sites. Journal of Hydrology 343:254-265, doi.
37. Lecoutre, B., 2005. Et si Vous Étiez un Bayésien qui S'ignore. Revue Modulad 32:92-105.
38. Lee, T.-S. and T.B.M.J. Ouarda, 2010. Long-Term Prediction of Precipitation and Hydrologic Extremes With Nonstationary Oscillation Processes. Journal of Geophysical Research 115:D13107, doi.
39. Martins, E.S. and J.R. Stedinger, 2000. Generalized Maximum Likelihood GEV Quantile Estimators for Hydrologic Data. Water Resources Research 36(3):737-744.
40. Metropolis, N., A. Rosenbluth, M. Rosenbluth, A. Teller, and E. Teller, 1953. Equations of State Calculations by Fast Computing Machines. Journal of Chemical Physics 21:1087-1092.
41. Olsen, J.R., J.R. Stedinger, N.C. Matalas, and E.Z. Stakhiv, 1999. Climate Variability and Flood Frequency Estimation for the Upper Mississippi and Lower Missouri Rivers. Journal of the American Water Resources Association 35(6):1509-1524.
42. Reis, D.S. and J.R. Stedinger, 2005. Bayesian MCMC Flood Frequency Analysis With Historical Information. Journal of Hydrology 313(1-2):97-116.
43. Reis, Jr., D.S., J.R. Stedinger, and E.S. Martins, 2005. Bayesian Generalized Least Squares Regression With Application to Log Pearson Type 3 Regional Skew Estimation. Water Resources Research 41:W10419, doi.
44. Ribatet, M., E. Sauquet, J.M. Grésillon, and T.B.M.J. Ouarda, 2007. Usefulness of the Reversible Jump Markov Chain Monte Carlo Model in Regional Flood Frequency Analysis. Water Resources Research 43:W08403, doi.
45. Robert, C. and G. Casella, 1999. Monte Carlo Statistical Methods. Springer-Verlag, New-York.
46. Sankarasubramanian, A. and U. Lall, 2003. Flood Quantiles in a Changing Climate: Seasonal Forecasts and Causal Relations? Water Resources Research 39(5):4-1-4-12.
47. Schwarz, G., 1978. Estimating the Dimension of a Model. Annals of Statistics 6:461-464.
48. Seidou, O. and T.B.M.J. Ouarda, 2007. Recursion-Based Multiple Changepoint Detection in Multivariate Linear Regression and Application to River Streamflows. Water Resources Research 43:W07404, 1-18, doi.
49. Seidou, O., T.B.M.J. Ouarda, M. Barbet, P. Bruneau, and B. Bobée, 2006. A Parametric Bayesian Combination of Local and Regional Information in Flood Frequency Analysis. Water Resources Research 42:W11408, 1-21, doi.
50. Smith, R.L., 1985. Maximum Likelihood Estimation in a Class of Non-Regular Cases. Biometrika 72:67-92.
51. Stephens, M., 2000. Bayesian Analysis of Mixture Models With an Unknown Number of Components - An Alternative to Reversible Jump Methods. Annals of Statistics 28:40-74.
52. Thiele, T.N., 1903. Theory of Observations. C. and E. Layton, London. Annals of Mathematical Statistics 2:165-308.
53. Yu, K. and R.A. Moyeed, 2001. Bayesian Quantile Regression. Statistics and Probability Letters 54:437-447.