Statistical analysis of extreme events in a nonstationary context via a Bayesian framework. Case study with peak-over-threshold data

Statistical analysis of extreme events in a nonstationary context via a Bayesian framework. Case study with peak-over-threshold data B. Renard, M. Lang, P. Bois To cite this version: B. Renard, M. Lang, P. Bois. Statistical analysis of extreme events in a nonstationary context via a Bayesian framework. Case study with peak-over-threshold data. Stochastic Environmental Research and Risk Assessment, Springer Verlag (Germany, 2006, 2 (2, p. 97 - p. 2. <0.007/s00477-006- 0047-4>. <hal-00452224> HAL Id: hal-00452224 https://hal.archives-ouvertes.fr/hal-00452224 Submitted on Feb 200 HAL is a multi-disciplinary open access archive for the deposit and dissemination of scientific research documents, whether they are published or not. The documents may come from teaching and research institutions in France or abroad, or from public or private research centers. L archive ouverte pluridisciplinaire HAL, est destinée au dépôt et à la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

Author-produced version of the article published in Stochastic environmental research and risk assessment, 2006, 2 (2, 97-2. The original publication is available at http://www.springerlink.com/ doi : 0.007/s00477-006-0047-4

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Sampling method POT Distribution Exponential Generalized Pareto Model stationary step-change linear trend exp M 0 exp M exp M 2 (t 0+ τ + 0+ > τ M 0 gp (t M gp 0+ τ 0+ > τ M 2 gp + Block Maximum Gumbel GEV M 0 gu (t M 0 gev (t M gu µ 0+ τ µ µ 0+ > τ gev M µ 0+ τ µ µ 0+ > τ,9"! M 2 gu µ µ + µ + gev M 2 µ µ + µ +

(a (b Model stationary step-change linear trend M 0 exp σ "%6 Specification on I "%6 M 0 gp σ + Specification on ( "%6 ( "%6 "%6 exp M σ "%6 Specification on "%6 "%6 M gp σ + Specification on ( "%6 ( "%6 "%6 ( "%6 exp M 2 σ + "%6 Specification on + "%6 "%6 + "%6 "%6 M 2 gp + σ + Specification on + ( "%6 + + + ( "%6 "%6 ( "%6 + + (c M 0 gu µ "%6"%6 Specification on "%6"%6 "%6 "%6 "%6 gu M µ "%6"%6 "%6"%6 "%6 "%6 "%6 "%6"%6 "%6 "%6 "%6 Specification on gu M 2 µ + µ + "%6"%6 Specification on + µ µ + "%6"%6 "%6"%6 "%6 "%6 + "%6 "%6 "%6 "%6 + µ µ + "%6"%6 "%6"%6 "%6 "%6 + "%6 "%6 "%6 "%6,9"!,

stationary Step change linear trend M 0 gev ( µ + "%6 Specification on "%6 ( "%6 ( "%6 "%6 ( "%6 "%6 M gev µ + ( "%6 Specification on ( "%6 ( "%6 "%6 ( "%6 "%6 ( "%6 ( "%6 "%6 M 2 gev ( + µ + µ + "%6 Specification on ( "%6 + + + µ µ + ( + "%6 "%6 + + ( "%6 "%6 ( "%6 + + + µ µ + ( + "%6 "%6,9"!9

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(a Density 4 3 2 Prior Post. (b Density 0. 0.05 0 0 2 4 Density 2 Post. Post. 2 (c Density 0 3 2 20 40 60 80 τ Prior 0 Post. 0 20 0 0 Density 30 2 3 Prior Post. 0 0 0.5.5 2 0 0.04 0 &. &, 0.04 0.035 0.03 Frequency 0.025 0.02 0.05 0.0 0.005 0 0 0 20 30 40 50 60 70 80 90 00 τ &"

0.2 0.8 posterior, model M 0 gp posterior 2, model M gp 0.6 0.4 prob 0.2 0. 0.08 0.06 0.04 0.02 0 0 5 0 5 20 25 &J &- 90 0year return flood (m 3.s 80 70 60 50 40 30 907 927 947 967 987 2007 2027 2047 2067 2087 207 years &#