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Book Sections Year : 2013

Bayesian methods for non-stationary extreme value analysis

Méthodes Bayésiennes pour l'analyse non-stationnaire des extrêmes

Benjamin Renard
X. Sun
  • Function : Author
M. Lang


Non-stationary models for extremes have attracted significant attention in recent years. The most common approach has been to introduce non-stationarity through the parameters of the extreme distribution, by using regression models linking parameter values with some time-varying covariate. This approach requires developing adapted estimation methods. In most cases, inference based on the likelihood has been favored over e.g. moment-based methods, due to its generality and flexibility to introduce various forms of non-stationarity [e.g., Coles et al., 2003]. In particular, 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 (and, as a consequence, of increasing complexity). We start in section 2 by a short introduction to Bayesian inference and related tools. This introduction is illustrated using the simplest possible case of estimating the parameters of an univariate and stationary distribution. In particular, section 2 will define the basic pieces forming Bayesian inference (likelihood function, prior, posterior and predictive distributions) and will briefly describe Monte-Carlo Markov Chain samplers, which are in practice the inseparable companions of the Bayesian Hydrologist. Section 3 will then illustrate the construction of at-site non-stationary models, using regression functions linking parameter values with time-varying covariates. The generality of this approach will be illustrated using several examples of non-stationary models. The difficulty of identifying non-stationary components based on the sole use of at-site data will also be discussed, and will motivate the construction of regional non-stationary models. Such models are presented in section 4 , and are based on the concept of “regional parameters”, i.e. parameters being assumed identical for all sites within an homogeneous region. The idea behind this assumption is to enable using data from several sites simultaneously in order to “share information” between sites and make the identification of non-stationary components more robust. 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, will be briefly presented. Lastly, section 5 discusses the generalization of such regional models, in order to make a less stringent assumption than the regional parameter assumption. This generalization is based on Bayesian hierarchical modeling, which has been recently applied in hydrological extreme analyses, and whose use is likely to grow in the future in the authors' opinion.
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Dates and versions

hal-02597485 , version 1 (15-05-2020)



Benjamin Renard, X. Sun, M. Lang. Bayesian methods for non-stationary extreme value analysis. Extremes in a Changing Climate: Detection, Analysis and Uncertainty, AghaKouchak, A.; Easterling, D.; Hsu, K.; Schubert, S.; Sorooshian, S. (Eds.), pp.39-95, 2013. ⟨hal-02597485⟩


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