### Printed in Great Britain Conditional simulation of max-stable processes

"... Since many environmental processes are spatial in extent, a single extreme event may affect several locations, and the spatial dependence must be taken into account in an appropriate way. This paper proposes a framework for conditional simulation of max-stable processes and gives closed forms for th ..."

Abstract
- Add to MetaCart

Since many environmental processes are spatial in extent, a single extreme event may affect several locations, and the spatial dependence must be taken into account in an appropriate way. This paper proposes a framework for conditional simulation of max-stable processes and gives closed forms for the regular conditional distributions of Brown–Resnick and Schlather processes. We test the method on simulated data and present applications to extreme rainfall around Zurich and extreme temperatures in Switzerland. The proposed framework provides accurate conditional simulations and can handle problems of realistic size.

### <hal-01134554>

, 2015

"... HAL is a multi-disciplinary open access archive for the deposit and dissemination of sci-entific research documents, whether they are pub-lished or not. The documents may come from teaching and research institutions in France or abroad, or from public or private research centers. L’archive ouverte p ..."

Abstract
- Add to MetaCart

(Show Context)
HAL is a multi-disciplinary open access archive for the deposit and dissemination of sci-entific research documents, whether they are pub-lished or not. The documents may come from teaching and research institutions in France or abroad, or from public or private research centers. L’archive ouverte pluridisciplinaire HAL, est destinée au dépôt et a ̀ la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d’enseignement et de recherche français ou étrangers, des laboratoires publics ou privés. Probabilities of concurrent extremes

### Journal de la Société Française de Statistique Extreme value copulas and max-stable processes Titre: Copules des valeurs extrêmes et processus max-stables

, 2012

"... Abstract: During the last decades, copulas have been increasingly used to model the dependence across several random variables such as the joint modelling of the intensity and the duration of rainfall storms. When the problem consists in modelling extreme values, i.e., only the tails of the distrib ..."

Abstract
- Add to MetaCart

(Show Context)
Abstract: During the last decades, copulas have been increasingly used to model the dependence across several random variables such as the joint modelling of the intensity and the duration of rainfall storms. When the problem consists in modelling extreme values, i.e., only the tails of the distribution, the extreme value theory tells us that one should consider max-stable distributions and put some restrictions on the copulas to be used. Although the theory for multivariate extremes is well established, its foundation is usually introduced outside the copula framework. This paper tries to unify these two frameworks in a single view. Moreover the latest developments on spatial extremes and max-stable processes will be introduced. At first glance the use of copulas for spatial problems sounds a bit odd but since usually stochastic processes are observed at a finite number of locations, the inferential procedure is intrinsically multivariate. An application on the spatial modelling of extreme temperatures in Switzerland is given. Results show that the use of non extreme value based models can largely underestimate the spatial dependence and the assumptions made on the spatial dependence structure should be chosen with care. Résumé : Les dernières décennies ont vu une utilisation des copules de plus en plus fréquente afin de modéliser la dépendance présente au sein d'un groupe de plusieurs variables aléatoires ; par exemple afin de modéliser simultanément l'intensité et la durée d'un événement pluvieux. Lorsque l'intérêt porte sur la modélisation des valeurs extrêmes, i.e., seulement les queues de la distribution, la théorie des valeurs extrêmes nous dicte quelles distributions considérer. Ces dernières doivent être max-stables et imposent donc des contraintes sur les copules adéquates. Bien que la théorie pour les extrêmes multivariées soit bien établie, elle est généralement introduite en dehors du cadre des copules. Ce papier essaye de présenter la théorie des valeurs extrêmes par le monde des copules. Les derniers développements sur les extrêmes spatiaux et les processus max-stables seront également évoqués. Bien qu'il paraisse étrange au premier abord de parler de copules pour les processus stochastiques, leur utilisation peut être adéquate puisque les processus sont souvent observés en un nombre fini de positions et la procédure d'estimation est alors intrinsèquement multivariée. Une application à la modélisation spatiale des températures extrêmes en Suisse est donnée. Les résultats montrent que l'utilisation de modèles non extrêmes peut largement sous-estimer la dépendance spatiale et que le choix fait sur la structure de dépendance spatiale est primordial.

### Attribution Analysis of Changes in Climate Extremes

, 2015

"... In inference for max-stable processes in regional frequency analysis, it is found that, when the dependence model is misspecified, the pairwise likelihood method leads to bias in estimating the shape parameter of the generalized extreme value (GEV) distribution. The bias can be serious when the depe ..."

Abstract
- Add to MetaCart

(Show Context)
In inference for max-stable processes in regional frequency analysis, it is found that, when the dependence model is misspecified, the pairwise likelihood method leads to bias in estimating the shape parameter of the generalized extreme value (GEV) distribution. The bias can be serious when the dependence is strong. Motivated by the fact that the primary interest in many studies is the inference about marginal GEV parameters and that the spatial dependence is a nuisance, we propose a combined score equations (CSE) approach that does not need dependence assumptions beyond the univariate GEV distribution. The CSE method combines the score equations of GEV model at each site with an approximate correlation function of the scores to improve the estimation efficiency. Applied to fingerprinting of changes in climate extremes with a coordinate descent algorithm to estimate a large number of parameters, the CSE method provides a close analog to the optimal fingerprinting in detection and attribution of changes in Zhuo Wang – University of Connecticut, 2015 climate extremes. The approach is applied on extreme temperature in Australia under

### Climate Change Impact on the Spatio-Temporal Variability of Hydro-Climate Extremes

"... by ..."

(Show Context)
### DOI: 10.1002/env.000 Spatial Extreme Value Analysis to Project Extremes of Large-Scale Indicators for Severe Weather

, 2013

"... Summary: Extreme weather is of great concern under a changing climate because of disproportional impacts on society. Most such events occur at scales that are too fine for global (or even most regional) climate models to resolve, making it difficult to infer potential future changes and impacts. One ..."

Abstract
- Add to MetaCart

Summary: Extreme weather is of great concern under a changing climate because of disproportional impacts on society. Most such events occur at scales that are too fine for global (or even most regional) climate models to resolve, making it difficult to infer potential future changes and impacts. One approach to analyzing severe weather in future climates is to consider larger-scale processes that are providing the setting for finer scale events. Concurrently high values of convective available potential energy (CAPE) and 0-6 km wind shear (Shear) have been found to represent conducive environments for severe weather. Here, we analyze these variables to determine how they might be used to project the spatial context of environments conducive to severe weather. Specific challenges include the fact that the data have strong spatial dependences, and analyzing extreme values over space is an active area of research. We take a new approach based on the Heffernan and Tawn conditional extreme value model. Results suggest that this technique excels at estimating the spatial behavior of CAPE and Shear largely because it allows for modeling their entire distribution, not just the extremes. A case study further examines these variables conditional on high river flow events, and it is found that distinct spatial patterns in the large-scale variables tend to exist concurrently with high river flow.

### CRPS M-ESTIMATION FOR MAX-STABLE MODELS

"... Max-stable random fields provide canonical models for the dependence of multivariate extremes. Inference with such models has been challenging due to the lack of tractable likelihoods. In contrast, the finite dimensional cumulative distribution functions (CDFs) are often readily available and natura ..."

Abstract
- Add to MetaCart

Max-stable random fields provide canonical models for the dependence of multivariate extremes. Inference with such models has been challenging due to the lack of tractable likelihoods. In contrast, the finite dimensional cumulative distribution functions (CDFs) are often readily available and natural to work with. Motivated by this fact, in this work we develop an M-estimation framework for max-stable models based on the continuous ranked probability score (CRPS) of multivariate CDFs. We start by establishing conditions for the consistency and asymptotic normality of the CRPS-based estimators in a general context. We then implement them in the max-stable setting and provide readily computable expressions for their asymptotic covariance matrices. The resulting point and asymptotic confidence interval estimates are illustrated over popular simulated models. They enjoy accurate coverages and offer an alternative to likelihood based methods. The new CRPS-based estimators were used to study rainfall extremes in Switzerland.

### MODELING SPATIAL EXTREMES VIA ENSEMBLE-OF-TREES OF PAIRWISE COPULAS

"... Assessing the risk of extreme events in a spatial domain, such as hurricanes, floods and droughts, presents unique sig-nificance in practice. Unfortunately, the existing extreme-value statistical models are typically not feasible for practical large-scale problems. Graphical models are capable of ha ..."

Abstract
- Add to MetaCart

(Show Context)
Assessing the risk of extreme events in a spatial domain, such as hurricanes, floods and droughts, presents unique sig-nificance in practice. Unfortunately, the existing extreme-value statistical models are typically not feasible for practical large-scale problems. Graphical models are capable of han-dling enormous number of variables, yet have not been ex-plored in the realm of extreme-value analysis. To bridge the gap, an extreme-value graphical model is introduced in this paper, i.e., ensemble-of-trees of pairwise copulas (ETPC). In the proposed graphical model, extreme-value marginal distri-butions are stitched together by means of pairwise copulas, which in turn are the building blocks of the ensemble of trees. By exploiting this particular structure, novel efficient infer-ence algorithms are derived that are applicable to large-scale statistical problems involving extreme values. It is proven that, under mild conditions, the ETPC model exhibits the fa-vorable property of tail-dependence between an arbitrary pair of sites (variables), and therefore is reliable to capture the de-pendence between extremes at different sites. Real data re-sults further demonstrate the advantages of the ETPC model. Index Terms — extreme events, pairwise copulas, graph-ical models, ensemble of trees, tail dependence 1.

### Australian North West Shelf

"... Multivariate challenges 3 Non-stationary extremes Penalised B-splines Quantile regression model for extreme value threshold Poisson model for rate of threshold exceedance Generalised Pareto model for size of threshold exceedance Return values 4 Current developments Extremal dependence Conditional ex ..."

Abstract
- Add to MetaCart

Multivariate challenges 3 Non-stationary extremes Penalised B-splines Quantile regression model for extreme value threshold Poisson model for rate of threshold exceedance Generalised Pareto model for size of threshold exceedance Return values 4 Current developments Extremal dependence Conditional extremes