Models and inference for uncertainty in extremal dependence

Coles, Stuart; Pauli, Francesco

doi:10.1093/biomet/89.1.183

Cited by 31 publications

(42 citation statements)

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“…For space-time data, hybrid models (Wadsworth and Tawn 2012) can capture different asymptotic properties at different distances and time lags, but they may be quite difficult to fit in practice. Coles and Pauli (2002) suggest an approach to merging the uncertainty arising from the dichotomy between the two types of asymptotic behavior, but it is unclear how it might be applied in the spatial context.…”

Section: Discussionmentioning

confidence: 99%

“…(3)) to model events above the 98 % quantile, u 98 , of the time series at each site separately, and used this fitted model to transform the data to have the unit Fréchet distribution. Since Bortot et al (2000) and Coles and Pauli (2002) have shown that the choice between asymptotic dependence and asymptotic independence models can influence extrapolation and association of extremes far more than the particular model used in each of these model classes, we fit only a limited selection of spatial correlations for this illustrative analysis. For each dataset, we used a censored pairwise threshold-based approach (Huser and Davison 2013) to fit three models to the exceedances over u 98 : (a) the max-stable Brown-Resnick model in Eq.…”

Section: Applicationsmentioning

confidence: 99%

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Geostatistics of Dependent and Asymptotically Independent Extremes

2013

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Spatial modeling of rare events has obvious applications in the environmental sciences and is crucial when assessing the effects of catastrophic events (such as heatwaves or widespread flooding) on food security and on the sustainability of societal infrastructure. Although classical geostatistics is largely based on Gaussian processes and distributions, these are not appropriate for extremes, for which maxstable and related processes provide more suitable models. This paper provides a brief overview of current work on the statistics of spatial extremes, with an emphasis on the consequences of the assumption of max-stability. Applications to winter minimum temperatures and daily rainfall are described.

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Section: Discussionmentioning

confidence: 99%

Section: Applicationsmentioning

confidence: 99%

Geostatistics of Dependent and Asymptotically Independent Extremes

2013

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“…Since this section gives a short conceptional overview of multivariate extreme value theory, in order to relate it to the copula approach for extreme value distributions, the reader is referred to Coles (2001); Coles and Pauli (2002); Beirlant et al (2004) and references therein for further reading.…”

Section: Extreme Value Copulasmentioning

confidence: 99%

Multivariate non-normally distributed random variables in climate research – introduction to the copula approach

Schölzel

Friederichs

2008

Nonlin. Processes Geophys.

287

178

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Abstract. Probability distributions of multivariate random variables are generally more complex compared to their univariate counterparts which is due to a possible nonlinear dependence between the random variables. One approach to this problem is the use of copulas, which have become popular over recent years, especially in fields like econometrics, finance, risk management, or insurance. Since this newly emerging field includes various practices, a controversial discussion, and vast field of literature, it is difficult to get an overview. The aim of this paper is therefore to provide an brief overview of copulas for application in meteorology and climate research. We examine the advantages and disadvantages compared to alternative approaches like e.g. mixture models, summarize the current problem of goodness-of-fit (GOF) tests for copulas, and discuss the connection with multivariate extremes. An application to station data shows the simplicity and the capabilities as well as the limitations of this approach. Observations of daily precipitation and temperature are fitted to a bivariate model and demonstrate, that copulas are valuable complement to the commonly used methods.

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“…[27] Lately, various models which jointly treat asymptotic dependence and independence have been proposed and studied [e.g., Coles and Pauli, 2002]. Here, we will pay a special attention to the work of Ledford and Ramos who extensively studied a very general framework to model the joint tail (survival function) defined by…”

Section: The Fragility Index Fi Inferencementioning

confidence: 99%

Spatial assessment of precipitation deficits in the Duero basin (central Spain) with multivariate extreme value statistics

2013

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[1] Nonirrigated agriculture on the Iberian Peninsula is regularly affected by dry periods that can cause important losses. This paper focuses on the comparison of the classical Standard Precipitation Index (SPI) with a fragility index developed by the multivariate extreme value theory community, which is used to describe monthly precipitation deficits below 30.5 mm (about 1 mm/d) in the Spanish Duero basin. The multivariate extreme value model allows to capture relevant information concerning the dependence structure among extreme precipitation deficits. Maps of those extremal dependence summaries and of loadings of principal components of the SPI provide quantitative information for water management. In addition, jointly analyzing data from several stations improves the inference of uncertainty. Spatial patterns of extremal dependence emerged with respect to orographic features. Most severe dry spells occur in the southeast of the Duero basin. In central plain of the Duero basin, a predominantly agricultural area, a strong fragility index for severity of dry spells is particularly found in eastern regions. Results of the MEVT and SPI analysis point in the same direction. Beyond this, the MEVT assessment gives a quantitative measure of the dependence between stations and regions. Estimates of return periods for extreme dry spell severity are discussed. Deficits below 42.7 mm are also analyzed.Citation: Kallache, M., P. Naveau, and M. Vrac (2013), Spatial assessment of precipitation deficits in the Duero basin (central Spain) with multivariate extreme value statistics, Water Resour. Res., 49,[6716][6717][6718][6719][6720][6721][6722][6723][6724][6725][6726][6727][6728][6729][6730]

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Models and inference for uncertainty in extremal dependence

Cited by 31 publications

References 0 publications

Geostatistics of Dependent and Asymptotically Independent Extremes

Geostatistics of Dependent and Asymptotically Independent Extremes

Multivariate non-normally distributed random variables in climate research – introduction to the copula approach

Spatial assessment of precipitation deficits in the Duero basin (central Spain) with multivariate extreme value statistics

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