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Predicting extreme events is important in many applications in risk analysis. The extreme-value theory suggests modelling extremes by max-stable distributions. The Bayesian approach provides a natural framework for statistical prediction.…
Extreme value analysis is an essential methodology in the study of rare and extreme events, which hold significant interest in various fields, particularly in the context of environmental sciences. Models that employ the exceedances of…
We propose a framework for studying predictability of extreme events in complex systems. Major conceptual elements -- direct cascading or fragmentation, spatial dynamics, and external driving -- are combined in a classical age-dependent…
Transitional localised turbulence in shear flows is known to either decay to an absorbing laminar state or proliferate via splitting. The average passage times from one state to the other depend super-exponentially on the Reynolds number…
Max-stable random fields play a central role in modeling extreme value phenomena. We obtain an explicit formula for the conditional probability in general max-linear models, which include a large class of max-stable random fields. As a…
In a wide variety of situations, anomalies in the behaviour of a complex system, whose health is monitored through the observation of a random vector X = (X1,. .. , X d) valued in R d , correspond to the simultaneous occurrence of extreme…
Invasion fronts in ecology are well studied but very few mathematical results concern the case with variable motility (possibly due to mutations). Based on an apparently simple reaction-diffusion equation, we explain the observed phenomena…
Inspired by birds flying through cluttered environments such as dense forests, this paper studies the theoretical foundations of a novel motion planning problem: high-speed navigation through a randomly-generated obstacle field when only…
Extreme events gain the attention of researchers due to their utmost importance in various contexts ranging from finance to climatology. This brings such recurrent events to the limelight of attention in interdisciplinary research. A…
Understanding the spatial extent of extreme precipitation is necessary for determining flood risk and adequately designing infrastructure (e.g., stormwater pipes) to withstand such hazards. While environmental phenomena typically exhibit…
A collection of identical and independent rare event first passage times is considered. The problem of finding the fastest out of $N$ such events to occur is called an extreme first passage time. The rare event times are singular and limit…
We model two time and space scales discrete observations by using a unique continuous diffusion process with time dependent coefficient. We define new parameters for the large scale model as functions of the small scale distribution…
Thermal soaring enables birds to perform cost-efficient flights during foraging or migration trips. Yet, although all soaring birds exploit vertical winds effectively, this group contains species that vary strongly in their morphologies.…
This paper develops likelihood-based methods for estimation, inference, model selection, and forecasting of continuous-time integer-valued trawl processes. The full likelihood of integer-valued trawl processes is, in general, highly…
We study a continuous time branching process where an individual splits into two daughters with rate b and dies with rate a, starting from a single individual at t=0. We show that the model can be mapped exactly to a random walk problem…
Due to complex physical phenomena, the distribution of heavy rainfall events is difficult to model spatially. Physically based numerical models can often provide physically coherent spatial patterns, but may miss some important…
Extreme value statistics provides accurate estimates for the small occurrence probabilities of rare events. While theory and statistical tools for univariate extremes are well-developed, methods for high-dimensional and complex data sets…
Full likelihood-based inference for high-dimensional multivariate extreme value distributions, or max-stable processes, is feasible when incorporating occurrence times of the maxima; without this information, $d$-dimensional likelihood…
We investigate extreme values of Mahonian and Eulerian distributions arising from counting inversions and descents of random elements of finite Coxeter groups. To this end, we construct a triangular array of either distribution from a…
This study provides a summary of the theory which enables the analysis of extreme values, i.e., of measurements acquired from the observation of extraordinary/rare physical phenomena. The formalism is developed in a transparent way,…