Dependence modelling for spatial extremes

Wadsworth, Jennifer L.; Tawn, Jonathan A.

doi:10.1093/biomet/asr080

Cited by 142 publications

(200 citation statements)

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“…This is consistent with the notion of asymptotic independence. Wadsworth & Tawn (2012) considered modelling asymptotic independence in spatial data. They demonstrated that a widely applicable class of models for such data is the so-called inverted max-stable process, which translates the lower tail of a max-stable copula to its upper tail.…”

Section: Discussionmentioning

confidence: 99%

“…There is realistically only one other such class in use, which consists of models constructed with zero-truncated Gaussian random fields (Schlather, 2002;Wadsworth & Tawn, 2012). The truncation makes calculation more awkward, though numerical approximations could in theory allow this.…”

Section: Discussionmentioning

confidence: 99%

“…There exists a slowly growing set of models for which the bivariate distributions are available; see, e.g., Schlather (2002), Kabluchko et al (2009 and Wadsworth & Tawn (2012). For such models, pairwise composite likelihood methods (Padoan et al, 2010) have become the standard for inference.…”

Section: Introductionmentioning

confidence: 99%

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Efficient inference for spatial extreme value processes associated to log-Gaussian random functions

2013

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SUMMARYMax-stable processes arise as the only possible nontrivial limits for maxima of affinely normalized identically distributed stochastic processes, and thus form an important class of models for the extreme values of spatial processes. Until recently, inference for max-stable processes has been restricted to the use of pairwise composite likelihoods, due to intractability of higherdimensional distributions. In this work we consider random fields that are in the domain of attraction of a widely used class of max-stable processes, namely those constructed via manipulation of log-Gaussian random functions. For this class, we exploit limiting d-dimensional multivariate Poisson process intensities of the underlying process for inference on all d-vectors exceeding a high marginal threshold in at least one component, employing a censoring scheme to incorporate information below the marginal threshold. We also consider the d-dimensional distributions for the equivalent max-stable process, and perform full likelihood inference by exploiting the methods of Stephenson & Tawn (2005), where information on the occurrence times of extreme events is shown to dramatically simplify the likelihood. The Stephenson-Tawn likelihood is in fact simply a special case of the censored Poisson process likelihood. We assess the improvements in inference from both methods over pairwise likelihood methodology by simulation.

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Section: Discussionmentioning

confidence: 99%

Section: Discussionmentioning

confidence: 99%

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Efficient inference for spatial extreme value processes associated to log-Gaussian random functions

2013

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“…By having a model that has both AD and AI components, we can avoid having to make this key decision. Wadsworth and Tawn [19] combine a max-stable process with an inverted max-stable process to construct a hybrid spatial dependence model. This model can capture both the AD and AI dependence structure but it is restricted in its forms of AD and AI that can be modeled.…”

Section: Introductionmentioning

confidence: 99%

“…This model can capture both the AD and AI dependence structure but it is restricted in its forms of AD and AI that can be modeled. Here we use the core structure of the Wadsworth and Tawn [19] model as a basis for exploring bivariate extreme value modeling in a new light. Specifically, we develop a distribution that contains both AD and AI components and has the flexibility to capture all dependence forms within very broad classes in each case.…”

Section: Introductionmentioning

confidence: 99%

Properties of extremal dependence models built on bivariate max-linearity

Kereszturi

Tawn

2017

Journal of Multivariate Analysis

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Please cite this article as: M. Kereszturi, J. Tawn, Properties of extremal dependence models built on bivariate max-linearity, Journal of Multivariate Analysis (2016), http://dx.doi.org/10. 1016/j.jmva.2016.12.001 This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain. Properties of extremal dependence models built on bivariate max-linearityMónika Kereszturi * and Jonathan Tawn STOR-i Centre for Doctoral Training, Lancaster University, UK AbstractBivariate max-linear models provide a core building block for characterizing bivariate max-stable distributions. The limiting distribution of marginally normalized component-wise maxima of bivariate max-linear models can be dependent (asymptotically dependent) or independent (asymptotically independent). However, for modeling bivariate extremes they have weaknesses in that they are exactly max-stable with no penultimate form of convergence to asymptotic dependence, and asymptotic independence arises if and only if the bivariate max-linear model is independent. In this work we present more realistic structures for describing bivariate extremes. We show that these models are built on bivariate max-linearity but are much more general. In particular, we present models that are dependent but asymptotically independent and others that are asymptotically dependent but have penultimate forms. We characterize the limiting behavior of these models using two new different angular measures in a radial-angular representation that reveal more structure than existing measures.

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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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Dependence modelling for spatial extremes

Cited by 142 publications

References 32 publications

Efficient inference for spatial extreme value processes associated to log-Gaussian random functions

Efficient inference for spatial extreme value processes associated to log-Gaussian random functions

Properties of extremal dependence models built on bivariate max-linearity

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

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