Combining Statistical and Expert Evidence within the D-S Framework: Application to Hydrological Return Level Estimation

  • Nadia Ben Abdallah
  • Nassima Mouhous Voyneau
  • Thierry Denœux
Part of the Advances in Intelligent and Soft Computing book series (AINSC, volume 164)


Estimation of extreme sea levels and waves for high return periods is of prime importance in hydrological design and flood risk assessment. The common practice consists of inferring design levels from the available observations and assuming the distribution of extreme values to be stationary. However, in the recent decades, more concern has been given to the integration of the effect of climate change in environmental analysis. When estimating defense structure design parameters, sea level rise projections provided by experts now have to be combined with historical observations. Due to limited knowledge about the future world and the climate system, and also to the lack of sufficient sea records, uncertainty involved in extrapolating beyond available data and projecting in the future is considerable and should absolutely be accounted for in the estimation of design values.

In this paper, we present a methodology based on evidence theory to represent statistical and expert evidence in the estimation of future extreme sea return level associated to a given return period. We represent the statistical evidence by likelihood-based belief functions [7] and the sea level rise projections provided by two sets of experts by a trapezoidal possibility distribution. A Monte Carlo simulation allows us to combine both belief measures to compute the future return level and a measure of the uncertainty of the estimations.


Return Period Flood Risk Generalize Extreme Value Return Level Belief Function 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Apel, H., Thikeken, A.H.: Flood risk assessment and associated uncertainty. Natural Hazards and Earth Sysem Sciences 4, 295–308 (2004)CrossRefGoogle Scholar
  2. 2.
    Aickin, M.: Connecting Dempster-Shafer belief functions with likelihood based inference. Synthese 123, 347–364 (2000)MathSciNetzbMATHCrossRefGoogle Scholar
  3. 3.
    Barnard, G.A., Jenkins, G.M., Winsten, C.B.: Likelihood inference and time series. Journal of the Royal Statistical Society 125(3), 321–372 (1962)CrossRefGoogle Scholar
  4. 4.
    Coles, S.G., Dixon, M.J.: Likelihood based inference for extreme value models. Extremes 2, 5–23 (1999)zbMATHCrossRefGoogle Scholar
  5. 5.
    Cox, D.R.: Some problems connected with statistical inference. Ann. Math. Statistics 29, 357–372 (1958)zbMATHCrossRefGoogle Scholar
  6. 6.
    Denoeux, T.: Maximum likelihood estimation from uncertain data in the belief function framework. IEEE Transactions on Knowledge and Data Engineering (to appear), doi:10.1109/TKDE.2011.201Google Scholar
  7. 7.
    Edwards, A.W.F.: Likelihood. University Press, Baltimore (1972)zbMATHGoogle Scholar
  8. 8.
    Fisher, R.A.: Inverse Probability and the use of likelihood. Proceedings of the Cambridge Philosophical Society 28, 257–261, CP3 (1932)CrossRefGoogle Scholar
  9. 9.
    Gumbel, E.J.: The statistics of extremes. Colombia University Press, New York (1958)Google Scholar
  10. 10.
  11. 11.
    Jenkinson, A.F.: The frequency distribution of the annual maximum (or minimum) values of meteorological elements. Quart. J. Roy. Meteo. Soc. 81, 158–171 (1955)CrossRefGoogle Scholar
  12. 12.
    Merz, B., et al.: Flood risk curves and uncertainty bounds. Natural Hazards 51, 437–458 (2009)CrossRefGoogle Scholar
  13. 13.
    Pfeffer, W., Harper, J., O’Neel, S.: Kinematic constraints on glacier contribution to 21st century sea level rise. Science 321, 1340–1430 (2008), doi:10.1126/science.1159099CrossRefGoogle Scholar
  14. 14.
    Purvis, M.: Probabilistic methodology to estimate future coastal flood risk due to sea level rise. Coastal Engineering 55, 1062–1073 (2008)CrossRefGoogle Scholar
  15. 15.
    Rhamstorf, S.: A semi empirical approach to projecting future sea level rise. Science 315, 368–370 (2007)CrossRefGoogle Scholar
  16. 16.
    Shafer, G.: A mathematical Theory of Evidence. Princeton University Press (1976)Google Scholar
  17. 17.
    Shafer, G.: Belief Functions and Parametric Models. Journal of the Royal Statistical Society. Series B. 44, 322–352 (1982)MathSciNetzbMATHGoogle Scholar
  18. 18.
    Xu, P., et al.: Uncertainty analysis in statistical modeling of extreme hydrological events. Stochastic Environmental Research and Risk Assessment 24, 567–578 (2010)CrossRefGoogle Scholar
  19. 19.
    Wasserman, L.: Belief functions and statistical inference. The Canadian Journal of Statistics 18, 183–196 (1990)MathSciNetzbMATHCrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Nadia Ben Abdallah
    • 1
  • Nassima Mouhous Voyneau
    • 2
  • Thierry Denœux
    • 1
  1. 1.CNRS, UMR 7253 HeudiasycUniversité de Technologie de CompiègneCompiègneFrance
  2. 2.Université de Technologie de CompiègneCompiègneFrance

Personalised recommendations