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A Bayesian Analysis of Extreme Rainfall Data

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  • Stuart G. Coles
  • Jonathan A. Tawn

Abstract

Understanding and quantifying the behaviour of a rainfall process at extreme levels has important applications for design in civil engineering. As in the extremal analysis of any environmental process, estimates often are required of the probability of events that are rarer than those already recorded. As data on extremes are scarce, all available sources of information should be used in inference. Consequently, research has focused on the development of techniques that make optimal use of available data. In this paper a daily rainfall series is analysed within a Bayesian framework, illustrating how the careful elicitation of prior expert information can supplement data and lead to improved estimates of extremal behaviour. For example, using the prior knowledge of an expert hydrologist, a Bayesian 95% interval estimate of the 100‐year return level for daily rainfall is found to be approximately half of the width of the corresponding likelihood‐based confidence interval.

Suggested Citation

  • Stuart G. Coles & Jonathan A. Tawn, 1996. "A Bayesian Analysis of Extreme Rainfall Data," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 45(4), pages 463-478, December.
    • Handle: RePEc:bla:jorssc:v:45:y:1996:i:4:p:463-478
    DOI: 10.2307/2986068
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    Cited by:

    1. Daniela Castro‐Camilo & Raphaël Huser & Håvard Rue, 2022. "Practical strategies for generalized extreme value‐based regression models for extremes," Environmetrics, John Wiley & Sons, Ltd., vol. 33(6), September.
    2. MacDonald, A. & Scarrott, C.J. & Lee, D. & Darlow, B. & Reale, M. & Russell, G., 2011. "A flexible extreme value mixture model," Computational Statistics & Data Analysis, Elsevier, vol. 55(6), pages 2137-2157, June.
    3. Palakorn Seenoi & Piyapatr Busababodhin & Jeong-Soo Park, 2020. "Bayesian Inference in Extremes Using the Four-Parameter Kappa Distribution," Mathematics, MDPI, vol. 8(12), pages 1-22, December.
    4. Hsieh, Ping-Hung, 2002. "An exploratory first step in teletraffic data modeling: evaluation of long-run performance of parameter estimators," Computational Statistics & Data Analysis, Elsevier, vol. 40(2), pages 263-283, August.
    5. Jeongwook Lee & Joon Jin Song & Yongku Kim & Jung In Seo, 2020. "Estimation and Prediction of Record Values Using Pivotal Quantities and Copulas," Mathematics, MDPI, vol. 8(10), pages 1-16, October.
    6. Hamid Mohtadi & Antu Panini Murshid, 2009. "Risk of catastrophic terrorism: an extreme value approach," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 24(4), pages 537-559.
    7. Eric T. Bradlow & Young-Hoon Park, 2007. "Bayesian Estimation of Bid Sequences in Internet Auctions Using a Generalized Record-Breaking Model," Marketing Science, INFORMS, vol. 26(2), pages 218-229, 03-04.
    8. Yingjie Wang & Xinsheng Liu, 2022. "A New Point Process Regression Extreme Model Using a Dirichlet Process Mixture of Weibull Distribution," Mathematics, MDPI, vol. 10(20), pages 1-24, October.
    9. Silvia Figini & Lijun Gao & Paolo Giudici, 2013. "Bayesian operational risk models," DEM Working Papers Series 047, University of Pavia, Department of Economics and Management.
    10. C J Scarrott & A MacDonald, 2010. "Extreme-value-model-based risk assessment for nuclear reactors," Journal of Risk and Reliability, , vol. 224(4), pages 239-252, December.
    11. Wang, Bing Xing & Ye, Zhi-Sheng, 2015. "Inference on the Weibull distribution based on record values," Computational Statistics & Data Analysis, Elsevier, vol. 83(C), pages 26-36.
    12. Ross Towe & Jonathan Tawn & Emma Eastoe & Rob Lamb, 2020. "Modelling the Clustering of Extreme Events for Short-Term Risk Assessment," Journal of Agricultural, Biological and Environmental Statistics, Springer;The International Biometric Society;American Statistical Association, vol. 25(1), pages 32-53, March.
    13. Tadele Akeba Diriba & Legesse Kassa Debusho, 2020. "Modelling dependency effect to extreme value distributions with application to extreme wind speed at Port Elizabeth, South Africa: a frequentist and Bayesian approaches," Computational Statistics, Springer, vol. 35(3), pages 1449-1479, September.
    14. Thomas Jagger & James Elsner & R. Burch, 2011. "Climate and solar signals in property damage losses from hurricanes affecting the United States," Natural Hazards: Journal of the International Society for the Prevention and Mitigation of Natural Hazards, Springer;International Society for the Prevention and Mitigation of Natural Hazards, vol. 58(1), pages 541-557, July.
    15. Farias, Rafael B.A. & Montoril, Michel H. & Andrade, José A.A., 2016. "Bayesian inference for extreme quantiles of heavy tailed distributions," Statistics & Probability Letters, Elsevier, vol. 113(C), pages 103-107.
    16. Brook T. Russell & Whitney K. Huang, 2021. "Modeling short‐ranged dependence in block extrema with application to polar temperature data," Environmetrics, John Wiley & Sons, Ltd., vol. 32(3), May.
    17. Xin Zhao & Carl Scarrott & Les Oxley & Marco Reale, 2010. "Extreme value modelling for forecasting market crisis impacts," Applied Financial Economics, Taylor & Francis Journals, vol. 20(1-2), pages 63-72.
    18. Ranjana Ray Chaudhuri & Prateek Sharma, 2020. "Addressing uncertainty in extreme rainfall intensity for semi-arid urban regions: case study of Delhi, India," Natural Hazards: Journal of the International Society for the Prevention and Mitigation of Natural Hazards, Springer;International Society for the Prevention and Mitigation of Natural Hazards, vol. 104(3), pages 2307-2324, December.
    19. Juan Gonzalez & Daniela Rodriguez & Mariela Sued, 2013. "Threshold selection for extremes under a semiparametric model," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 22(4), pages 481-500, November.
    20. Wang, Bing Xing & Yu, Keming & Coolen, Frank P.A., 2015. "Interval estimation for proportional reversed hazard family based on lower record values," Statistics & Probability Letters, Elsevier, vol. 98(C), pages 115-122.
    21. Mary Kynn, 2008. "The ‘heuristics and biases’ bias in expert elicitation," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 171(1), pages 239-264, January.

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