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Bayesian Extreme Value Theory

In: Extreme Value Theory with Applications to Natural Hazards

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  • Nicolas Bousquet

    (EDF R & D)

Abstract

This chapter provides an introduction to Bayesian statistical theory and a broad review of its application to extreme values. The Bayesian methodology differs greatly from the traditional approaches considered in the other chapters. Indeed, it requires the construction of so-called prior measures for the parameters of extreme value models and defines estimation through the minimization of a cost function adapted to the event. While Bayesian calculations (as those based on Monte Carlo Markov Chains) remain superficially discussed, this chapter focuses on modeling features, which allow expert opinion and historical knowledge to be integrated into the estimation of quantities of interest. In this respect, the Bayesian approach constitutes a methodology of increasing use, allowing the mixed treatment of aleatoric and epidemic uncertainties and adapted to the specific needs of engineers.

Suggested Citation

  • Nicolas Bousquet, 2021. "Bayesian Extreme Value Theory," Springer Books, in: Nicolas Bousquet & Pietro Bernardara (ed.), Extreme Value Theory with Applications to Natural Hazards, chapter 0, pages 271-325, Springer.
    • Handle: RePEc:spr:sprchp:978-3-030-74942-2_11
    DOI: 10.1007/978-3-030-74942-2_11
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