Bayesian Inference for Extremes: Accounting for the Three Extremal Types

Stephenson, Alec; Tawn, Jonathan A.

doi:10.1007/s10687-004-3479-6

Cited by 60 publications

(60 citation statements)

References 34 publications

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“…The most popular include the maximum likelihood (e.g., [34]), probability weighted moments (e.g., [41]), L-moments (e.g., [42]), and Bayesian methods (e.g., [43]). Without carrying out a comparative study of these methods, we merely describe briefly the maximum likelihood method used in the present work.…”

Section: Time-varying Distributionmentioning

confidence: 99%

Temperature Extremes: Estimation of Non-Stationary Return Levels and Associated Uncertainties

Hamdi¹,

Duluc²,

Rebour³

2018

Atmosphere

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Estimating temperature extremes (TEs) and associated uncertainties under the non-stationary (NS) assumption is a key research question in several domains, including the nuclear safety field. Methods for estimating TEs and associated confidence intervals (CIs) have often been used in the literature but in a stationary context, separately and without detailed comparison. The extreme value theory is often used to assess risks in a context of climate change. It provides an accurate indication of distributions describing the frequency of occurrence of TEs. However, in an NS context, the notion of the return period is not easily interpretable. For instance, to predict a high return level (RL) in a future year, time-varying distributions must be used and compared. This study examines the performance of a new concept to predict RLs in an NS context and compares three methods for constructing the associated CIs (delta, profile likelihood, and parametric bootstrap). The present work takes up the concept of integrated return periods that define the T-year RL as the level for which the expected number of events in a T-year period is one and proposes a new method based on conditional predictions that is useful for predicting high RLs of extreme events in the near future (the 100-year RL in the year 2030, for instance). The daily maximum temperature (DMT) observed at the Orange Station in France was used as a case study. Several trend models were compared and a new likelihood-based method to detect breaks in TEs is proposed. The analyses were conducted assuming the time-varying Generalized Extreme Value (GEV) distribution. The concepts have been implemented in a software package (Non-Stationary Generalized Extreme Value (NSGEV)). The application demonstrates that the RL estimates for NS situations can be quite different from those corresponding to stationary conditions. Overall, the results suggest that the NS analysis can be helpful in making a more appropriate assessment of the risk for periodic safety reviews during the life of a nuclear power plant (NPP).

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Section: Time-varying Distributionmentioning

confidence: 99%

Temperature Extremes: Estimation of Non-Stationary Return Levels and Associated Uncertainties

Hamdi¹,

Duluc²,

Rebour³

2018

Atmosphere

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“…In contrast, probabilistic models developed from the field of extreme value statistics draw inferences about the extremes using data from relatively extreme values alone. Such statistical models are sensitive to the choice of the distribution and the fitting procedures (Woth et al 9 2006), nevertheless, they are frequently utilized in analyses of extreme tides and/or surges (Lowe et al 2001;Butler et al 2007;Stephenson and Tawn 2004) and are used here.…”

Section: Statistical Approach To Extreme Value Analysismentioning

confidence: 99%

Tide–surge interactions and their effects on total sea levels in Irish coastal waters

2013

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“…Coles & Tawn (1996) utilizaram conhecimentos de profissionais que trabalham na área para construir suas informações à priori, as quais incorporam a dependência entre os parâmetros associados ao modelo extremo, podendo incorporar o conhecimento baseado em quantis com uma distribuição Gama. Stephenson (2002) e Stephenson & Tawn (2004), sugerem um procedimento Bayesiano para incorporar o conhecimento prévio na estrutura dos teoremas de modelos na inferência de valores extremos, reduzindo a incerteza da estimação dos parâmetros.…”

Section: (Recebido Em 27 De Abril De 2006 E Aprovado Em 26 De Março Dunclassified

Análise Bayesiana no estudo do tempo de retorno das precipitações pluviais máximas em Jaboticabal (SP)

2009

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RESUMODados históricos de precipitação máxima são utilizados para realizar previsões de chuvas extremas, cujo conhecimento é de grande importância na elaboração de projetos agrícolas e de engenharia hidráulica. A distribuição generalizada de valores extremos (GEV) tem sido aplicada com freqüência nesses tipos de estudos, porém, algumas dificuldades na obtenção de estimativas confiáveis sobre alguma medida dos dados têm ocorrido devido ao fato de que, na maioria das situações, tem-se uma quantidade escassa de dados. Uma alternativa para obter melhorias na qualidade das estimativas seria utilizar informações dos especialistas de determinada área em estudo. Sendo assim, objetiva-se neste trabalho analisar a aplicação da Inferência Bayesiana com uma distribuição a priori baseada em quantis extremos, que facilite a incorporação dos conhecimentos fornecidos por especialistas, para obter as estimativas de precipitação máxima para os tempos de retorno de 10 e 20 anos e seus respectivos limites superiores de 95%, para o período anual e para os meses da estação chuvosa em Jaboticabal (SP). A técnica Monte Carlo, via Cadeias de Markov (MCMC), foi empregada para inferência a posteriori de cada parâmetro. A metodologia Bayesiana apresentou resultados mais acurados e precisos, tanto na estimação dos parâmetros da distribuição GEV, como na obtenção dos valores de precipitação máxima provável para a região de Jaboticabal, apresentando-se como uma boa alternativa na incorporação de conhecimentos a priori no estudo de dados extremos. Termos para indexação:Inferência bayesiana, distribuição a priori, conhecimento a priori, quantis extremos, técnica Monte Carlo via Cadeias de Markov, precipitação pluvial máxima. ABSTRACTHistorical maximum rainfall data are used to forecast extreme rainfall, which is important to elaborate agricultural and hydraulic engineering projects. Generalized Extreme Value Distribution (GEV) has been applied in such type of studies. Since those values are extracted from the upper (or lower) tail of the original distribution, a scarce amount of data is obtained in most cases, which may be a problem acquiring reliable estimates about some measure of interest. An alternative to overcome this potential problem would be the use of information available from experts in the area. Therefore, this paper intended to analyze the application of the Bayesian Inference using a priori distribution based on extreme quantiles, which facilitates the incorporation of the information supplied by the experts in order to determine the punctual and the 95% upper limit estimates of the probable maximum precipitation for return periods of 10 and 20 years, yearly and monthly in Jaboticabal, São Paulo State, Brazil. Markov Chain Monte Carlo (MCMC) methods were used to a posterior inference of each parameter. Bayesian inference yielded more suitable and accurate results in the estimation of the parameters of the GEV distribution as well as in the determination of the values of the probable maximum precipitation estimates for Jaboticabal...

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Bayesian Inference for Extremes: Accounting for the Three Extremal Types

Cited by 60 publications

References 34 publications

Temperature Extremes: Estimation of Non-Stationary Return Levels and Associated Uncertainties

Temperature Extremes: Estimation of Non-Stationary Return Levels and Associated Uncertainties

Tide–surge interactions and their effects on total sea levels in Irish coastal waters

Análise Bayesiana no estudo do tempo de retorno das precipitações pluviais máximas em Jaboticabal (SP)

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