Kick-off Workshop

12 noon: Welcome Lunch Buffet
13h30- 14h : Opening (T. Opitz, A. Sabourin, G. Stupfler)
14h - 16h: Session with scientific talks
- Johan Segers
- Juliette Legrand
- Clément Dombry
16h-18h30: Coffee break and time for informal discussions

6 June:

9h: Welcome Coffee
9h20-12h30: Session with scientific talks
- Antoine Chambaz
- Antoine Marchina
- Alexis Boulin
- Antoine Usseglio-Carleve
12h30 : Lunch Buffet
13h30-15h30: Poster Session
15h30-17h00 : Session with scientific talks
- Nicolas Meyer
- Mathieu Vrac

7 June:

9h Welcome Coffee
9h30-11h30: Session with scientific talks
- Pavlo Mozharovsyi
- Nathan Huet
- Mikael Escobar-Bach
11h30-12h30 Discussions
12h30 Lunch Buffet and Closing

Participants

Samira Aka, Antoine Chambaz, Fabienne Comte, Marine Demangeot, Antoine Doizé, Clément Dombry, Holger Drees, Jonathan El Methni, Mikael Escobar-Bach, Carlos Fernandez, Laurent Gardes, Stéphane Girard, Anja Janssen, Marie Kratz, Juliette Legrand, Laurie Leterrier, Stéphane Lhaut, Hadrien Lorenzo, Rita Maatouk, Perla Mallouk, Alexandre Mansire, Antoine Marchina, Maud Megret, Nicolas Meyer, Reshma Mohane, Anas Mourahib, Théo Moins, Philippe Naveau, Thomas Opitz, Jean Pachebat, Sylvie Parey, Mike Pereira, Romain Pic, Alex Podgorny, Anne Sabourin, Johan Segers, Sibsankar Singha, Gilles Stupfler, Soulivanh Thao, Charles Tillier

Posters

Samira Aka, Stéphane Lhaut, Hadrien Lorenzo, Anas Mourahib, Alex Podgorny, Sibsankar Singha

Funding

ANR PRC grant EXSTA

INRAE-INRIA ANOVEX project

Talks

Alexis Boulin, Université Côté d'Azur. "Estimating regularly varying random vectors with discrete exponent measure via model-based clustering.

Abstract: This study introduces a novel estimation method for the entries and structure of a matrix A in the linear factor model X = AZ + E. This is applied to an observable vector X in R^d with Z in R^K, a vector composed of independently regularly varying random variables, and light-tailed independent noise E in R^d. X is hence regularly varying and its exponent measure is subsequently discrete and completely characterized by the matrix A. Each row of the matrix A is supposed to be both scaled and sparse. Additionally, the value of K is not known a priori. The problem of identifying the matrix A from its matrix of pairwise extremal correlation is addressed. In the presence of pure variables, which are elements of X linked, through A, to a single latent factor, the matrix A can be reconstructed from the extremal correlation matrix. Our proofs of identifiability are constructive and pave the way for our innovative estimation for determining the number of factors K and the matrix A from n weakly dependent observations on X.

Antoine Chambaz, Université Paris-Cité. "Presentation of "Causal discovery in heavy-tailed models" by Gnecco et al., The Annals of Statistics, 49(3), 2021"

Abstract: In this talk, I will present the work of Gnecco et al. (The Annals of Statistics, 49(3), 2021) on causal discovery in heavy-tailed models.

Clément Dombry, Université de Franche-Comté. "Asymptotic theory for Bayesian inference and prediction in the Peaks-Over-Threshold method".

Abstract: The Peaks Over Threshold (POT) method is the most popular statistical method for the analysis of univariate extremes. Even though there is a rich applied literature on Bayesian inference for the POT method there is no asymptotic theory for such proposals. Even more importantly, the ambitious and challenging problem of predicting future extreme events according to a proper probabilistic forecasting approach has received no attention to date. In this paper we develop the asymptotic theory (consistency, contraction rates, asymptotic normality and asymptotic coverage of credible intervals) for the Bayesian inference based on the POT method. We extend such an asymptotic theory to cover the Bayesian inference on the tail properties of the conditional distribution of a response random variable conditionally to a vector of random covariates. With the aim to make accurate predictions of severe extreme events than those occurred in the past, we specify the posterior predictive distribution of a future unobservable excess variable in the unconditional and conditional approach and we prove that is Wasserstein consistent and derive its contraction rates. Simulations show the good performances of the proposed Bayesian inferential methods. The analysis of the change in the frequency of financial crises over time shows the utility of our methodology.
Joint work with Simone A. Padoan, Stefano Rizzelli (preprint arXiv:2310.06720)

Mikael Escobar-Bach, Université d'Angers. "Survival analysis and insufficient follow-up: an approach based on extreme values".

Abstract: Survival analysis can be related to the modeling of cure individuals, i.e. subjects that will never experience the event of interest. However, most estimation methods proposed so far in the literature do not handle the case of insufficient follow-up, that is when the support of the censoring time is strictly less than that of the survival time of the susceptible subjects, which results in a lack of identifiability in parametric models. In this talk, I intend to show how extrapolation techniques from extreme value theory can help in this context by proposing several approaches for the approximations of the model functions. Their asymptotic properties will be discussed as well as their applicability with simulations and real data applications.
Joint work with Ross Maller, Xie Ping, Ingrid Van Keilegom and Muzhi Zao.

Nathan Huet, Télécom Paris, Institut polytechnique de Paris. "Joint Modeling Extremal Sea-Levels Dependency across different French Atlantic Coast Stations"

Abstract: Appropriate modeling of extreme sea levels is crucial, particularly for coastal risk management. Our study focuses on modeling extreme sea levels along the French Atlantic coast, with a particular emphasis on investigating the extremal dependence structure between stations. We employ the peak-over-threshold framework, where a multivariate extreme event is defined whenever at least one location records a large value, though not necessarily all stations simultaneously. We investigate two approaches separately. First, we utilize the Multivariate Generalized Pareto Distribution (MGPD) to model these extremes, which is well-suited for this type of analysis. Given the beneficial properties of this distribution, we derive a generative model for extreme sea levels at a station conditionally based on extreme values at other nearby stations. Second, we examine the point estimate performance of a novel extreme regression model. This specific regression framework enables accurate point predictions using only the 'angle' of input variables, i.e., input variables divided by their norms.The ultimate objective of this work is to reduce the uncertainty behind risk management quantities (e.g., return values) at stations with limited historical records by incorporating new data based on extreme sea levels from stations with longer records, such as Brest and Saint-Nazaire, which have over 150 years of records. Joint work with Philippe Naveau and Anne Sabourin.

Juliette Legrand, LMBA, Université de Bretagne Occidentale. " Nonparametric simulation of multivariate dependent extremes"

Abstract : Stochastic simulation of extreme events in a multivariate setting is of great interest to capture not only the statistical behaviour of the extremes, but also the dependence between large values of complex processes. Based on multivariate EVT, we present two nonparametric simulation algorithms of bivariate generalised Pareto distributed variables. These algorithms allow for both joint and conditional simulation of bivariate asymptotically dependent extremes. The second part of this talk will be dedicated to the extension of the two former algorithms to the multivariate case (d>2). These extensions can improve the estimation of various risk measures at extreme levels by increasing the number of available extreme samples. The algorithms' performances are demonstrated using both simulated and real data applications. Joint work with P. Ailliot, P. Naveau and N. Raillard (first part) & N. Madhar and M. Thomas (second part).

Antoine Marchina, MAP5, Université Paris-Cité. " Concentration inequalities for extreme value analysis"

Abstract : Concentration inequalities for functionals of independent random variables are a fundamental tool in the analysis of various problems in statistics or learning theory. In this talk, I will present some classical concentration results, including Talagrand’s inequalities for the suprema of empirical processes, and then show how they can be used for extreme value analysis.

Nicolas Meyer, Université de Montpellier. "Modeling moderate and extreme rainfall at high spatio-temporal resolution"

Abstract: Flood risk analysis in an urban environment requires a precise understanding of rainfall events. We will present the specific case of the Montpellier region, in which a network of rain gauges from the Montpellier Urban Observatory enables us to carry out an initial study based on data for the period 2019-2022. As rainfall events are rare (but intense) in this region, only few data are available. Therefore, we enrich the existing dataset with a stochastic rainfall generator. We will present the main steps in the construction of this generator: simulation of marginals according to the extended generalized Pareto distribution, simulation of the spatio-temporal dependence structure via a Brown-Resnick or r-Pareto process, taking into account physical constraints such as wind via advection. This leads to a full model for rainfall events for which we propose a statistical analysis. This is a joint work with Chloé Serre-Combe, Thomas Opitz, and Gwladys Toulemonde.

Pavlo Mozharovsyi, LTCI, Télécom Paris, Institut Polytechnique de Paris. " Distributionally robust halfspace depth "

Abstract: Tukey's halfspace depth can be seen as a stochastic program and as such it is not guarded against optimizer's curse, so that a limited training sample may easily result in a poor out-of-sample performance. We propose a generalized halfspace depth concept relying on the recent advances in distributionally robust optimization, where every halfspace is examined using the respective worst-case distribution in the Wasserstein ball of a positive radius centered at the empirical law. This new depth can be seen as a smoothed and regularized classical halfspace depth which is retrieved as the ball's radius tends towards zero. It inherits most of the main properties of the latter and, additionally, enjoys various new attractive features such as continuity and strict positivity beyond the convex hull of the support. We provide numerical illustrations of the new depth and its advantages, and develop some fundamental theory. In particular, we study the upper level sets and the median region including their breakdown properties.

Johan Segers, Université Catholique de Louvain . " Tail calibration of probabilistic forecasts "

Abstract: Probabilistic forecasts comprehensively describe the uncertainty in the unknown future outcome, making them essential for decision making and risk management. While several methods have been introduced to evaluate probabilistic forecasts, existing evaluation techniques are ill-suited to the evaluation of tail properties of such forecasts. However, these tail properties are often of particular interest to forecast users due to the severe impacts caused by extreme outcomes. In this work, we reinforce previous results related to the deficiencies of proper scoring rules when evaluating forecast tails, demonstrating that even classes of scoring rules cannot compare forecasts with regards to tail behavior. Alternative methods to evaluate forecasts for extreme events are therefore required. To this end, we introduce a general notion of tail calibration for probabilistic forecasts, which allows forecasters to assess the reliability of their predictions for extreme outcomes. We study the relationships between tail calibration and standard notions of forecast calibration, and discuss connections to peaks over threshold models in extreme value theory. Diagnostic tools are introduced and applied in a case study on European precipitation forecasts. Joint work with Sam Allen (ETH Zurich), Jonathan Koh (University of Bern), Johan Segers (UCLouvain), Johanna Ziegel (ETH Zurich).

Antoine Usseglio-Carlève, Avignon Université. "Bias-reduced and variance-corrected asymptotic Gaussian Inference about extreme expectiles"

Abstract: The expectile is a prime candidate for being a standard risk measure in actuarial and financial contexts, for its ability to recover information about probabilities and typical behavior of extreme values, as well as its excellent axiomatic properties. A series of recent papers has focused on expectile estimation at extreme levels, with a view on gathering essential information about low-probability, high-impact events that are of most interest to risk managers. The obtention of accurate confidence intervals for extreme expectiles is paramount in any decision process in which they are involved, but actual inference on these tail risk measures is still a difficult question due to their least squares nature and sensitivity to tail heaviness. This article focuses on asymptotic Gaussian inference about tail expectiles in the challenging context of heavy-tailed observations. We use an in-depth analysis of the proofs of asymptotic normality results for two classes of extreme expectile estimators to derive bias-reduced and variance-corrected Gaussian confidence intervals. These, unlike previous attempts in the literature, are well-rooted in statistical theory and can accommodate underlying distributions that display a wide range of tail behaviors. A large-scale simulation study and three real data analyses confirm the versatility of the proposed technique.

Mathieu Vrac, LSCE–IPSL. "Compound Extreme 'Hot & Dry' Climate Events: Are changes already visible in France?"

Abstract: Many climate-related disasters result from a combination of several climate phenomena, also referred to as “compound events’’ (CEs). By interacting with each other, these phenomena can lead to huge environmental and societal impacts, at a scale potentially far greater than any of these climate events could have caused separately. Marginal and dependence properties of the climate phenomena forming the CEs are key statistical properties characterising their probabilities of occurrence.
In this talk, we assess the time of emergence of bivariate “hot & dry” (H&D) CE probabilities over France within the 1950-2022 time period, which is critical for mitigation strategies and adaptation planning. Using copula theory, we separate and quantify the contribution of the marginal and dependence properties to the overall probability changes of multivariate hazards leading to CEs. It provides a better understanding of how the statistical properties of temperature and precipitation leading to H&D CEs evolve and contribute to the change in their occurrences. It is therefore possible to ask ourselves: Can we already see changes in H&D probabilities within the last few decades? Where and when did the signal emerge? Are there geographical patterns? Which component (“hot”? “dry”?) contributes the most to changes in H&D probabilities?
The results highlight the importance of considering changes in both marginal and dependence properties, both for understanding past changes and for future risk assessments related to CEs.
This is joint work with Joséphine Schmutz and Bastien François.

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