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Bayesian posterior predictive return levels for environmental extremes

Lookup NU author(s): Dr Lee Fawcett, Dr Amy Green



This work is licensed under a Creative Commons Attribution 4.0 International License (CC BY 4.0).


A key aim of most extreme value analyses is the estimation of the r-year return level; the wind speed, or sea-surge, or rainfall level (for example), we might expect to see once (on average) every r years. There are compelling arguments for working within the Bayesian setting here, not least the natural extension to prediction via the posterior predictive distribution. Indeed, for practitioners the posterior predictive return level has been cited as perhaps the most useful point summary from a Bayesian analysis of extremes, and yet little is known of the properties of this statistic. Inthis paper, we attempt to assess the performance of predictive return levels relative to their estimative counterparts obtained directly from the return level posterior distribution; in particular, we make comparisons with the return level posterior mean, mode and 95% credible upper bound. Differences between the predictive return level and standard summaries from the return level posterior distribution, for wind speed extremes observed in the UK, motivates this work. A large scale simulation study then reveals the superiority of the predictive return level over the other posterior summaries in many cases of practical interest.

Publication metadata

Author(s): Fawcett L, Green AC

Publication type: Article

Publication status: Published

Journal: Stochastic Environmental Research and Risk Assessment

Year: 2018

Volume: 32

Issue: 8

Pages: 2233-2252

Print publication date: 01/08/2018

Online publication date: 31/05/2018

Acceptance date: 11/05/2018

Date deposited: 04/06/2018

ISSN (print): 1436-3240

ISSN (electronic): 1436-3259

Publisher: Springer


DOI: 10.1007/s00477-018-1561-x


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