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dc.contributor.authorCastro-Camilo, Daniela
dc.contributor.authorHuser, Raphaël
dc.contributor.authorRue, Haavard
dc.date.accessioned2021-06-27T13:52:24Z
dc.date.available2021-06-27T13:52:24Z
dc.date.issued2021-06-24
dc.identifier.urihttp://hdl.handle.net/10754/669796
dc.description.abstractThe generalised extreme value (GEV) distribution is a three parameter family that describes the asymptotic behaviour of properly renormalised maxima of a sequence of independent and identically distributed random variables. If the shape parameter ξ is zero, the GEV distribution has unbounded support, whereas if ξ is positive, the limiting distribution is heavy-tailed with infinite upper endpoint but finite lower endpoint. In practical applications, we assume that the GEV family is a reasonable approximation for the distribution of maxima over blocks, and we fit it accordingly. This implies that GEV properties, such as finite lower endpoint in the case ξ > 0, are inherited by the finite-sample maxima, which might not have bounded support. This is particularly problematic when predicting extreme observations based on multiple and interacting covariates. To tackle this usually overlooked issue, we propose a blended GEV distribution, which smoothly combines the left tail of a Gumbel distribution (GEV with ξ = 0) with the right tail of a Fréchet distribution (GEV with ξ > 0) and, therefore, has unbounded support. Using a Bayesian framework, we reparametrise the GEV distribution to offer a more natural interpretation of the (possibly covariate-dependent) model parameters. Independent priors over the new location and spread parameters induce a joint prior distribution for the original location and scale parameters. We introduce the concept of property-preserving penalised complexity (P3C) priors and apply it to the shape parameter to preserve first and second moments. We illustrate our methods with an application to NO2 pollution levels in California, which reveals the robustness of the bGEV distribution, as well as the suitability of the new parametrisation and the P3C prior framework.
dc.description.sponsorshipWe thank Sabrina Vettori for providing a simplified version of the pollution data. We acknowledge Lars Holden for the notion of blending at the distribution level, an idea that came to light during a hallway conversation 20 years ago. This publication is partially based upon work supported by the King Abdullah University of Science and Technology (KAUST) Office of Sponsored Research (OSR) under Award No. OSR-CRG2017-3434.
dc.publisherarXiv
dc.relation.urlhttps://arxiv.org/pdf/2106.13110.pdf
dc.rightsArchived with thanks to arXiv
dc.titlePractical strategies for GEV-based regression models for extremes
dc.typePreprint
dc.contributor.departmentStatistics Program
dc.contributor.departmentComputer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division
dc.eprint.versionPre-print
dc.contributor.institutionSchool of Mathematics and Statistics, University of Glasgow, UK.
dc.identifier.arxivid2106.13110
kaust.personHuser, Raphaël
kaust.personRue, Haavard
kaust.grant.numberOSR-CRG2017-3434
refterms.dateFOA2021-06-27T13:54:16Z
kaust.acknowledged.supportUnitCRG
kaust.acknowledged.supportUnitOffice of Sponsored Research (OSR)


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