Related papers: A dynamic extreme value model with applications to…
Extreme environmental phenomena such as major precipitation events manifestly exhibit spatial dependence. Max-stable processes are a class of asymptotically-justified models that are capable of representing spatial dependence among extreme…
When passing from the univariate to the multivariate setting, modelling extremes becomes much more intricate. In this introductory exposition, classical multivariate extreme value theory is presented from the point of view of multivariate…
The Generalized Extreme Value (GEV) distribution plays a critical role in risk assessment across various domains, such as hydrology, climate science, and finance. In this study, we investigate its application in analyzing intraday trading…
We consider discrete time dynamical systems and show the link between Hitting Time Statistics (the distribution of the first time points land in asymptotically small sets) and Extreme Value Theory (distribution properties of the partial…
Extreme geophysical events are of crucial relevance to our daily life: they threaten human lives and cause property damage. To assess the risk and reduce losses, we need to model and probabilistically predict these events. Parametrizations…
I propose a new procedure to estimate the False Alarm Probability, the measure of significance for peaks of periodograms. The key element of the new procedure is the use of generalized extreme-value distributions, the limiting distribution…
This paper leverages the statistics of extreme values to predict the worst-case convergence times of machine learning algorithms. Timing is a critical non-functional property of ML systems, and providing the worst-case converge times is…
Observed accidents have been the main resource for road safety analysis over the past decades. Although such reliance seems quite straightforward, the rare nature of these events has made safety difficult to assess, especially for new and…
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),…
Recently, a marked Poisson process (MPP) model for life catastrophe risk was proposed in [6]. We provide a justification and further support for the model by considering more general Poisson point processes in the context of extreme value…
The frequency of disruptive and newly emerging threats (e.g. man-made attacks--cyber and physical attacks; extreme natural events--hurricanes, earthquakes, and floods) has escalated dramatically in the last decade. Impacts of these events…
The extreme values theory presents specific tools for modeling and predicting extreme phenomena. In particular, risk assessment is often analyzed through measures for tail dependence and high values clustering. Despite technological…
Extreme environmental events such as severe storms, drought, heat waves, flash floods, and abrupt species collapse have become more prevalent in the earth-atmosphere dynamic system in recent years. In order to fully understand the…
Many scientific and engineering problems require accurate models of dynamical systems with rare and extreme events. Such problems present a challenging task for data-driven modelling, with many naive machine learning methods failing to…
We introduce a method to estimate simultaneously the tail and the threshold parameters of an extreme value regression model. This standard model finds its use in finance to assess the effect of market variables on extreme loss distributions…
Modeling cyber risks has been an important but challenging task in the domain of cyber security. It is mainly because of the high dimensionality and heavy tails of risk patterns. Those obstacles have hindered the development of statistical…
A central problem in uncertainty quantification is how to characterize the impact that our incomplete knowledge about models has on the predictions we make from them. This question naturally lends itself to a probabilistic formulation, by…
Fluctuations of global additive quantities, like total energy or magnetization for instance, can in principle be described by statistics of sums of (possibly correlated) random variables. Yet, it turns out that extreme values (the largest…
We propose a transformation capable of altering the tail properties of a distribution, motivated by extreme value theory, which can be used as a layer in a normalizing flow to approximate multivariate heavy tailed distributions. We apply…
We present a new volatility model, simple to implement, that includes a leverage effect whose return-volatility correlation function fits to empirical observations. This model is able to capture both the "retarded effect" induced by the…