Related papers: Extreme value methods for estimating rare events i…
The task of simplifying the complex spatio-temporal variables associated with climate modeling is of utmost importance and comes with significant challenges. In this research, our primary objective is to tailor clustering techniques to…
When applying multivariate extreme value statistics to analyze tail risk in compound events defined by a multivariate random vector, one often assumes that all dimensions share the same extreme value index. While such an assumption can be…
Turbulent flow fields are characterized by extreme events that are statistically intermittent and carry a significant amount of energy and physical importance. To emulate these flows, we introduce the extreme variational Autoencoder (xVAE),…
Extreme value theory is concerned with probabilistic and statistical questions related to very high or very low values in sequences of random variables and in stochastic processes. The subject has a rich mathematical theory and also a long…
This paper focuses on rare events associated with the tail probabilities of the extremal eigenvalues in the $\beta$-Jacobi ensemble, which plays a critical role in both multivariate statistical analysis and statistical physics. Under the…
Causal dependence modelling of multivariate extremes is intended to improve our understanding of the relationships amongst variables associated with rare events. Regular variation provides a standard framework in the study of extremes. This…
The contribution of this paper is to introduce change of measure based techniques for the rare-event analysis of heavy-tailed stochastic processes. Our changes-of-measure are parameterized by a family of distributions admitting a mixture…
Extreme weather events are widely studied in fields such as agriculture, ecology, and meteorology. The spatio-temporal co-occurrence of extreme events can strengthen or weaken under changing climate conditions. In this paper, we propose a…
In this paper, we discuss the application of extreme value theory in the context of stationary $\beta$-mixing sequences that belong to the Fr\'echet domain of attraction. In particular, we propose a methodology to construct bias-corrected…
Many real-world processes have complex tail dependence structures that cannot be characterized using classical Gaussian processes. More flexible spatial extremes models exhibit appealing extremal dependence properties but are often…
An unmanned autonomous vehicle (UAV) is sent on a mission to explore and reconstruct an unknown environment from a series of measurements collected by Bayesian optimization. The success of the mission is judged by the UAV's ability to…
We develop methods, based on extreme value theory, for analysing observations in the tails of longitudinal data, i.e., a data set consisting of a large number of short time series, which are typically irregularly and non-simultaneously…
Multivariate extreme value analysis quantifies the probability and magnitude of joint extreme events. River discharges from the upper Danube River basin provide a challenging dataset for such analysis because the data, which is measured on…
Extreme value theory for univariate and low-dimensional observations has been explored in considerable detail, but the field is still in an early stage regarding high-dimensional settings. This paper focuses on H\"usler-Reiss models, a…
Adaptation-relevant predictions of climate change are often derived by combining climate model simulations in a multi-model ensemble. Model evaluation methods used in performance-based ensemble weighting schemes have limitations in the…
In extreme value analysis, tail behavior of a heavy-tailed data distribution is modeled by a Pareto-type distribution in which the so-called extreme value index (EVI) controls the tail behavior. For heavy-tailed data obtained from multiple…
Estimation of tail quantities, such as expected shortfall or Value at Risk, is a difficult problem. We show how the theory of nonlinear expectations, in particular the Data-robust expectation introduced in [5], can assist in the…
We propose a method for the accurate estimation of rare event or failure probabilities for expensive-to-evaluate numerical models in high dimensions. The proposed approach combines ideas from large deviation theory and adaptive importance…
A recently introduced general-purpose heuristic for finding high-quality solutions for many hard optimization problems is reviewed. The method is inspired by recent progress in understanding far-from-equilibrium phenomena in terms of {\em…
We consider a class of chance-constrained programs in which profit needs to be maximized while enforcing that a given adverse event remains rare. Using techniques from large deviations and extreme value theory, we show how the optimal value…