Bayesian Methods for Non-stationary Extreme Value Analysis

  • Benjamin Renard
  • Xun Sun
  • Michel Lang
Part of the Water Science and Technology Library book series (WSTL, volume 65)


Non-stationary models for extremes have attracted significant attention in recent years. These models require adapted estimation methods. Bayesian inference offers an attractive framework to estimate non-stationary models and, importantly, to quantify estimation and predictive uncertainties.

This chapter therefore focuses on the application of Bayesian inference to non-stationary extreme models. It is organized as a step-by-step building of non-stationary models of increasing generality. The principles of Bayesian inference are introduced using the simple case of a univariate and stationary distribution. The construction of at-site non-stationary models, using regression functions linking parameter values with time-varying covariates, is then presented. The difficulty of identifying non-stationary components based on the sole use of at-site data is also discussed, and motivates the construction of regional non-stationary models. Such models are based on the concept of “regional parameters”, i.e. parameters being assumed identical for all sites within a homogeneous region. The inference of regional models poses an additional difficulty compared to the at-site approach: the existence of spatial dependences makes the derivation of the inference equations challenging. A practical solution, based on the use of spatial copulas, is briefly presented. Lastly, a generalization of the “regional parameter” paradigm, based on Bayesian hierarchical modeling, is discussed.


Posterior Distribution Markov Chain Monte Carlo Prior Distribution Bayesian Inference Generalize Extreme Value 
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.



Part of this work is funded by the French Research Agency (ANR) through the project EXTRAFLO ( Météo France is gratefully acknowledged for providing the data.


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© Springer Science+Business Media Dordrecht 2013

Authors and Affiliations

  1. 1.Irstea, UR HHLY, Hydrology-HydraulicsLyonFrance

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