A full Bayesian approach to generalized maximum likelihood estimation of generalized extreme value distribution

Yoon, Sang Pil; Cho, Woncheol; Heo, Jun Haeng; Kim, Chul Eung

doi:10.1007/s00477-009-0362-7

Cited by 28 publications

(16 citation statements)

References 33 publications

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“…Recently, an alternative to these, employing a full Bayesian GEV estimation method which contains a semi-Bayesian framework of generalized maximum likelihood estimators and considers the shape, location and scale parameters as random variables were developed (Yoon et al 2010). However, these approaches do not consider non-stationarity.…”

Section: Generalized Extreme Value Modelsmentioning

confidence: 99%

Long-term time-dependent stochastic modelling of extreme waves

Vanem

2010

Stoch Environ Res Risk Assess

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This paper presents a literature survey on timedependent statistical modelling of extreme waves and sea states. The focus is twofold: on statistical modelling of extreme waves and space-and time-dependent statistical modelling. The first part will consist of a literature review of statistical modelling of extreme waves and wave parameters, most notably on the modelling of extreme significant wave height. The second part will focus on statistical modelling of time-and space-dependent variables in a more general sense, and will focus on the methodology and models used also in other relevant application areas. It was found that limited effort has been put on developing statistical models for waves incorporating spatial and long-term temporal variability and it is suggested that model improvements could be achieved by adopting approaches from other application areas. In particular, Bayesian hierarchical space-time models were identified as promising tools for spatio-temporal modelling of extreme waves. Finally, a review of projections of future extreme wave climate is presented.

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Section: Generalized Extreme Value Modelsmentioning

confidence: 99%

Long-term time-dependent stochastic modelling of extreme waves

Vanem

2010

Stoch Environ Res Risk Assess

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“…Park (2005) recommended to use α = 2.5 and β = 2.5. Yoon et al (2010) considered a full Bayesian approach for the selection of HP. We denote the MPLEs using CD, MS, and Park penalties as the MPLE-CD, MPLE-MS, and MPLE-P, respectively.…”

Section: Maximum Penalized Likelihood Estimationmentioning

confidence: 99%

A data-adaptive maximum penalized likelihood estimation for the generalized extreme value distribution

Lee

Shin

Park

2017

CSAM

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Maximum likelihood estimation (MLE) of the generalized extreme value distribution (GEVD) is known to sometimes over-estimate the positive value of the shape parameter for the small sample size. The maximum penalized likelihood estimation (MPLE) with Beta penalty function was proposed by some researchers to overcome this problem. But the determination of the hyperparameters (HP) in Beta penalty function is still an issue. This paper presents some data adaptive methods to select the HP of Beta penalty function in the MPLE framework. The idea is to let the data tell us what HP to use. For given data, the optimal HP is obtained from the minimum distance between the MLE and MPLE. A bootstrap-based method is also proposed. These methods are compared with existing approaches. The performance evaluation experiments for GEVD by Monte Carlo simulation show that the proposed methods work well for bias and mean squared error. The methods are applied to Blackstone river data and Korean heavy rainfall data to show better performance over MLE, the method of L-moments estimator, and existing MPLEs.

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“…The parameter ξ is called the shape parameter; the related location‐scale family H ξ , μ , σ ( x ) can be introduced by replacing the argument x mentioned earlier by ( x ‐ μ )/ σ and adjusting the support accordingly. Parameters are usually estimated via maximum likelihood techniques or Bayesian methods (Coles, ; Yoon et al ., ). One of the most critical issues in the block‐maxima approach is the determination of the block size.…”

Section: Introductionmentioning

confidence: 99%

Risk management against extremes in a changing environment: a risk‐layer approach using copulas

Hochrainer‐Stigler

Pflug

2012

Environmetrics

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Assessing and managing extreme risk have to be carried out differently compared with frequent event risk. Especially dependencies among risks are important to be incorporated here. Additionally, dynamics that may alter risk in the future are important to be included in modeling approaches so that strategies to reduce risk are sustainable in the long run. However, little is known about changing risks under dynamic conditions and corresponding advantages and limits of options to decrease or hedge risks. We use this knowledge gap as our starting point to lay out an approach how to model dependencies with the use of copulas and how to manage and prevent increases in risk because of dynamic changes over time. The uniqueness of these approaches is that changes in anticipated losses over different spatial scales (or risks) compared with the current situation are separated into different risk layers, and these different risk layers can be expressed simultaneously with loss distributions. Because risk‐reduction and risk‐transfer measures are suitable for different risk layers, this distinction can serve in determining the most appropriate risk management measures over different scales. We apply our method to flood risk in Hungary, specifically within the Tisza region. The approach may be particularly useful if dissimilar changes in risk at the local level can be expected, for example, an increase in low‐probability events in one region and an increase in the frequency of small magnitude events in a neighboring region. Copyright © 2012 John Wiley & Sons, Ltd.

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A full Bayesian approach to generalized maximum likelihood estimation of generalized extreme value distribution

Cited by 28 publications

References 33 publications

Long-term time-dependent stochastic modelling of extreme waves

Long-term time-dependent stochastic modelling of extreme waves

A data-adaptive maximum penalized likelihood estimation for the generalized extreme value distribution

Risk management against extremes in a changing environment: a risk‐layer approach using copulas

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