A Hierarchical Model for Extreme Wind Speeds

Fawcett, Lee; Walshaw, David

doi:10.1111/j.1467-9876.2006.00557.x

Cited by 47 publications

(43 citation statements)

References 14 publications

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“…Such models are very flexible and recently their use in modeling extreme data has been increasing. See for example, Fawcett and Walshaw (2006), Cooley et al (2006Cooley et al ( , 2007, Mendes et al (2008). Methodological study of strategies for Bayesian hierarchical models for block maxima data, can be found in Sang (2008).…”

Section: Bayesian Hierarchical Modelsmentioning

confidence: 99%

“…This dependence structure is then modeled by a latent spatial process through the model parameters. Typically, data, conditional on the realizations of this latent process as well as other explanatory variables, are assumed to be independent, but not identical, although more complicated Markov structures can also be assumed (Fawcett and Walshaw 2006). See also Sang (2008) for ways of introducing dependence structure in the likelihood using a Gaussian copula.…”

Section: Bayesian Hierarchical Modelsmentioning

confidence: 99%

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Asymptotic models and inference for extremes of spatio-temporal data

Turkman

Pereira

2009

Extremes

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Recently there has been a lot of effort to model extremes of spatially dependent data. These efforts seem to be divided into two distinct groups: the study of max-stable processes, together with the development of statistical models within this framework; the use of more pragmatic, flexible models using Bayesian hierarchical models (BHM) and simulation based inference techniques. Each modeling strategy has its strong and weak points. While max-stable models capture the local behavior of spatial extremes correctly, hierarchical models based on the conditional independence assumption, lack the asymptotic arguments the max-stable models enjoy. On the other hand, they are very flexible in allowing the introduction of physical plausibility into the model. When the objective of the data analysis is to estimate return levels or kriging of extreme values in space, capturing the correct dependence structure between the extremes is crucial and max-stable processes are better suited for these purposes. However when the primary interest is to explain the sources of variation in extreme events Bayesian hierarchical modeling is a very flexible tool due to the ease with which random effects are incorporated in the model. In this paper we model a data set on Portuguese wildfires to show the flexibility of BHM in incorporating spatial dependencies acting at different resolutions.

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Section: Bayesian Hierarchical Modelsmentioning

confidence: 99%

Section: Bayesian Hierarchical Modelsmentioning

confidence: 99%

Asymptotic models and inference for extremes of spatio-temporal data

Turkman

Pereira

2009

Extremes

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“…Smith (1999) considers predictive inference under the Bayesian and frequentist paradigms, and Smith and Goodman (2000) and Bottolo et al (2003) construct Bayesian hierarchical models for extreme values in insurance problems. Fawcett and Walshaw (2006a) model extreme wind speeds in a region of the UK using a Bayesian hierarchical model. Fawcett and Walshaw (2006b) consider Bayesian inference for Markov chain models (also for extreme wind speeds) using a simulation framework similar to that used by Smith et al (1997), outlined in Section 2.3, to obtain estimates of the extremal index.…”

Section: Bayesian Methodsmentioning

confidence: 99%

Bayesian inference for clustered extremes

Fawcett

Walshaw

2008

Extremes

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We consider Bayesian inference for the extremes of dependent stationary series. We discuss the virtues of the Bayesian approach to inference for the extremal index, and for related characteristics of clustering behaviour. We develop an inference procedure based on an automatic declustering scheme, and using simulated data we implement and assess this procedure, making inferences for the extremal index, and for two cluster functionals. We then apply our procedure to a set of real data, specifically a time series of windspeed measurements, where the clusters correspond to storms. Here the two cluster functionals selected previously correspond to the mean storm length and the mean inter-storm interval. We also consider inference for long-period return levels, advocating the posterior predictive distribution as being most representative of the information required by engineers interested in design level specifications.

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“…Since the first proposal of the Markov Chain Monte Carlo (MCMC) (Gelfand and Smith 1990), several studies have successfully applied the Bayesian method to the frequency analysis of extreme wind speed (Fawcett and Walshaw 2006), extreme precipitation (Coles and Tawn 1996;Coles and Pericchi 2003;Cooley et al 2007), and floods (Ribatet et al 2007;Lima and Lall 2010;Liang et al 2012;Viglione et al 2013). Cooley et al (2006) first proposed a comprehensive Bayesian hierarchical model for lichenometry.…”

Section: Introductionmentioning

confidence: 99%

A regional Bayesian hierarchical model for flood frequency analysis

Yan

Moradkhani

2014

Stoch Environ Res Risk Assess

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In this study, we propose a regional Bayesian hierarchical model for flood frequency analysis. The Bayesian method is an alternative to the traditional regional flood frequency analysis. Instead of relying on the delineation of implicit homogeneous regions, the Bayesian hierarchical method describes the spatial dependence in its inner structure. Similar to the classical Bayesian hierarchical model, the process layer of our model presents the spatial variability of the parameters by considering different covariates (e.g., drainage area, elevation, precipitation). Beyond the three classical layers (data, process, and prior) of the Bayesian hierarchical model, we add a new layer referred to as the ''L-moments layer''. The L-moments layer uses L-moments theory to select the best-fit probability distribution based on the available data. This new layer can overcome the subjective selection of the distribution based on extreme value theory and determine the distribution from the data instead. By adding this layer, we can combine the merits of regional flood frequency and Bayesian methods. A standard process of covariates selection is also proposed in the Bayesian hierarchical model. The performance of the Bayesian model is assessed by a case study over the Willamette River Basin in the Pacific Northwest, U.S. The uncertainty of different flood percentiles can be quantified from the posterior distributions using the Markov Chain Monte Carlo method. Temporal changes for the 100-year flood percentiles are also examined using a 20-and 30-year moving window method. The calculated shifts in flood risk can aid future water resources planning and management.

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A Hierarchical Model for Extreme Wind Speeds

Cited by 47 publications

References 14 publications

Asymptotic models and inference for extremes of spatio-temporal data

Asymptotic models and inference for extremes of spatio-temporal data

Bayesian inference for clustered extremes

A regional Bayesian hierarchical model for flood frequency analysis

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