A hierarchical max-stable spatial model for extreme precipitation

Reich, Brian J.; Shaby, Benjamin A.

doi:10.1214/12-aoas591

Cited by 134 publications

(185 citation statements)

References 43 publications

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“…Based on these few observed differences, the ETP could be recommended for the spatial extrapolation of the 100-years return level, while the BRP should be preferred for the estimation of the extremal coefficient. The HKEVP of Reich and Shaby (2012) has the particularity of performing well on both criteria for each of the hierarchical generators. Its main drawback seems to be its poor robustness when fitted on classical max-stable generators.…”

Section: Resultsmentioning

confidence: 99%

“…The Hierarchical Kernel Extreme Value Process (HKEVP) has been introduced by Reich and Shaby (2012) and further developed in Shaby and Reich (2012) and Reich et al (2014). It is defined as follows.…”

Section: The Hierarchical Kernel Extreme Value Process: Hkevpmentioning

confidence: 99%

“…The kernels ω(·) used in Reich and Shaby (2012) are rescaled Gaussian densities. More precisely, let V := {v 1 , .…”

Section: The Hierarchical Kernel Extreme Value Process: Hkevpmentioning

confidence: 99%

“…In our case, one estimation with this model on the real or artificial dataset takes around 30 minutes and one hour respectively with LVM and HKEVP. The model of Reich and Shaby (2012) is thus the heaviest in this case and the computational time increases with the number of sites n and the number of knots L.…”

Section: Bayesian Modelsmentioning

confidence: 99%

“…Indeed, all values of the random effect are updated at each MCMC step, which represents L × T parameters. The impact of a misspecification of the knots set has been studied in Reich and Shaby (2012). The conclusions can be summarized saying that too few knots may lead to a larger bias in the estimation of the GEV parameters, while considering too many knots than necessary does not improve significantly these estimations but increases the computational time drastically.…”

Section: More About the Hkevpmentioning

confidence: 99%

See 4 more Smart Citations

Modeling extreme rainfall A comparative study of spatial extreme value models

2017

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In this paper, focus is done on spatial models for extreme events and on their respective efficiency regarding the estimation of two risk measures: one extrapolating marginal distributions and one summarizing the spatial bivariate dependence of extremes. A wide comparison is performed on an innovative simulation plan that has been specifically designed from a daily precipitation data set. The objective of this paper is twofold: firstly, pointing out the inherent properties of each model, and secondly, advising users on how to choose the model depending on the specific type of risk.

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Section: Resultsmentioning

confidence: 99%

Section: The Hierarchical Kernel Extreme Value Process: Hkevpmentioning

confidence: 99%

“…The kernels ω(·) used in Reich and Shaby (2012) are rescaled Gaussian densities. More precisely, let V := {v 1 , .…”

Section: The Hierarchical Kernel Extreme Value Process: Hkevpmentioning

confidence: 99%

Section: Bayesian Modelsmentioning

confidence: 99%

Section: More About the Hkevpmentioning

confidence: 99%

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Modeling extreme rainfall A comparative study of spatial extreme value models

2017

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Combining regional estimation and historical floods: A multivariate semiparametric peaks‐over‐threshold model with censored data

Sabourin

Renard²

2015

Water Resources Research

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The estimation of extreme flood quantiles is challenging due to the relative scarcity of extreme data compared to typical target return periods. Several approaches have been developed over the years to face this challenge, including regional estimation and the use of historical flood data. This paper investigates the combination of both approaches using a multivariate peaks-over-threshold model that allows estimating altogether the intersite dependence structure and the marginal distributions at each site. The joint distribution of extremes at several sites is constructed using a semiparametric Dirichlet Mixture model. The existence of partially missing and censored observations (historical data) is accounted for within a data augmentation scheme. This model is applied to a case study involving four catchments in Southern France, for which historical data are available since 1604. The comparison of marginal estimates from four versions of the model (with or without regionalizing the shape parameter; using or ignoring historical floods) highlights significant differences in terms of return level estimates. Moreover, the availability of historical data on several nearby catchments allows investigating the asymptotic dependence properties of extreme floods. Catchments display a significant amount of asymptotic dependence, calling for adapted multivariate statistical models.

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Spatial Bayesian hierarchical modeling of precipitation extremes over a large domain

Bracken

Rajagopalan

Cheng

et al. 2016

Water Resources Research

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We propose a Bayesian hierarchical model for spatial extremes on a large domain. In the data layer a Gaussian elliptical copula having generalized extreme value (GEV) marginals is applied. Spatial dependence in the GEV parameters is captured with a latent spatial regression with spatially varying coefficients. Using a composite likelihood approach, we are able to efficiently incorporate a large precipitation data set, which includes stations with missing data. The model is demonstrated by application to fall precipitation extremes at approximately 2600 stations covering the western United States, −125°E to −100°E longitude and 30°N–50°N latitude. The hierarchical model provides GEV parameters on a 1/8° grid and, consequently, maps of return levels and associated uncertainty. The model results indicate that return levels and their associated uncertainty have a well‐defined spatial structure. Maps of return levels provide information about the spatial variations of the risk of extreme precipitation in the western US and is expected to be useful for infrastructure planning.

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A hierarchical max-stable spatial model for extreme precipitation

Cited by 134 publications

References 43 publications

Modeling extreme rainfall A comparative study of spatial extreme value models

Modeling extreme rainfall A comparative study of spatial extreme value models

Combining regional estimation and historical floods: A multivariate semiparametric peaks‐over‐threshold model with censored data

Spatial Bayesian hierarchical modeling of precipitation extremes over a large domain

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