Extremes from scarce data: The role of Bayesian and scaling techniques in reducing uncertainty

Sánchez‐Arcilla, Agustín; Aguar, Jesus Gomez; Egozcue, J. J.; Ortego, M. I.; Γαλιατσάτου, Παναγιώτα; Prinos, P.

doi:10.1080/00221686.2008.9521956

Cited by 29 publications

(12 citation statements)

References 13 publications

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“…A proper threshold can be obtained by plottingê(u) as a function of the threshold u and identifying the lowest value of threshold above whichê(u) increases approximately linearly. This plot has been implemented in practice by Hogg and Klugman [47], Begueria [48], Sanchez-Arcilla et al [49], among others.…”

Section: Mean Excess Plotmentioning

confidence: 99%

Directional Extreme Value Models in Wave Energy Applications

2020

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A wide range of wave energy applications relies on the accurate estimation of extreme wave conditions, while some of them are frequently affected by directionality. For example, attenuators and terminators are the most common types of wave energy converters whose performance is highly influenced by their orientation with respect to the prevailing wave direction. In this work, four locations in the eastern Mediterranean Sea are selected with relatively high wave energy flux values and extreme wave heights are examined with wave direction as a covariate. The Generalized Pareto distribution is used to model the extreme values of wave height over a pre-defined threshold, with its parameters being expressed as a function of wave direction through Fourier series expansion. In order to be consistent with the analysis obtained from the independent fits for directional sectors, the estimation of parameters is based on a penalized maximum likelihood criterion that ensures a good agreement between the two approaches. The obtained results validate the integration of directionality in extreme value models for the examined locations and design values of significant wave height are provided with respect to direction for the 50- and 100-year return period with bootstrap confidence intervals.

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Section: Mean Excess Plotmentioning

confidence: 99%

Directional Extreme Value Models in Wave Energy Applications

2020

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“…Galiatsatou [19] uses the three abovementioned estimation procedures to calculate the parameters of the margins of a bivariate distribution of extreme wave heights and storm surges, considering the cases of full and asymptotic dependence. Galiatsatou and Prinos [20], Galiatsatou et al [21] and Sánchez -Arcilla et al [22] consider the effects of different methods of estimation of the marginal distributions of rainfall, surge and wave height data, respectively, on the return levels of the studied process.…”

Section: The Implementation Of the Multivariate Extreme Valuementioning

confidence: 99%

“…Standard Markov chain Monte Carlo methods routinely allow the approximation of integrals such as the one in the denominator of equation (4). More details about the Bayesian methodology used here are given in Galiatsatou and Prinos [20], Galiatsatou et al [21] and Sánchez-Arcilla et al [22].…”

Section: The Bayesian Approachmentioning

confidence: 99%

Bivariate Analysis of Extreme Wave and Storm Surge Events. Determining the Failure Area of Structures

Γαλιατσάτου¹

2011

TOOEJ

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In the present paper a bivariate process of extreme waves and storm surges at a Dutch station on the North Sea is considered. A bivariate logistic model and a sequential estimation procedure are used to extract joint exceedance probabilities of the two variables. The parameters of the margins of the bivariate distribution are defined by three different methods of estimation: a) the Maximum Likelihood Estimation (MLE) approach, b) a Bayesian procedure with flat prior distributions and c) the L-Moments (LM) estimation procedure. Comparison of the results of the three methods is performed and general conclusions are extracted. An approach to estimate the failure area of a particular structure under extreme sea conditions is presented, using the margins resulting from the three different estimation methods.

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“…This assumption is based on the fact that, on Planet Earth, wind speed is physically limited and, accordingly, the existence of such upper bound is granted, even though the limit itself is not known. This assumption has been successfully applied in the extremal analysis of other weather magnitudes, such as rainfall and ocean-wave heights Egozcue et al, 2005Egozcue et al, , 2006Sánchez-Arcilla et al, 2008a).…”

Section: Event Magnitude Modelmentioning

confidence: 99%

“…Bayesian methods were introduced in the field of natural hazards two decades ago and they have succeeded as a flexible and consistent way of controlling uncertainty (Sánchez-Arcilla et al, 2008a;Coles and Tawn, 1996;Gelman et al, 1995). Simultaneously, the models for analysing extremal events have evolved.…”

Section: Introductionmentioning

confidence: 99%

Bayesian trend analysis of extreme wind using observed and hindcast series off the Catalan coast, NW Mediterranean Sea

Ortego

Egozcue

Tolosana‐Delgado

2014

Nat. Hazards Earth Syst. Sci.

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Abstract. It has been suggested that climate change might modify the occurrence rate and magnitude of large oceanwave and wind storms. The hypothesised reason is the increase of available energy in the atmosphere-ocean system. Forecasting models are commonly used to assess these effects, given that good-quality data series are often too short. However, forecasting systems are often tuned to reproduce the average behaviour, and there are concerns on their relevance for extremal regimes. We present a methodology of simultaneous analysis of observed and hindcast data with the aim of extracting potential time drifts as well as systematic regime discrepancies between the two data sources. The method is based on the peak-over-threshold (POT) approach and the generalized Pareto distribution (GPD) within a Bayesian estimation framework. In this context, storm events are considered points in time, and modelled as a Poisson process. Storm magnitude over a reference threshold is modelled with a GPD, a flexible model that captures the tail behaviour of the magnitude distribution.All model parameters, i.e. shape and location of the magnitude GPD and the Poisson occurrence rate, are affected by a trend in time. Moreover, a systematic difference between parameters of hindcast and observed series is considered. Finally, the posterior joint distribution of all these trend parameters is studied using a conventional Gibbs sampler. This method is applied to compare hindcast and observed series of average wind speed at a deep buoy location off the Catalan coast (NE Spain, western Mediterranean; buoy data from 2001; REMO wind hindcasting from 1958 on). Appropriate scale and domain of attraction are discussed, and the reliability of trends in time is addressed.

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Extremes from scarce data: The role of Bayesian and scaling techniques in reducing uncertainty

Cited by 29 publications

References 13 publications

Directional Extreme Value Models in Wave Energy Applications

Directional Extreme Value Models in Wave Energy Applications

Bivariate Analysis of Extreme Wave and Storm Surge Events. Determining the Failure Area of Structures

Bayesian trend analysis of extreme wind using observed and hindcast series off the Catalan coast, NW Mediterranean Sea

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