Related papers: Sparse Structures for Multivariate Extremes
This article presents methods for estimating extreme probabilities, beyond the range of the observations. These methods are model-free and applicable to almost any sample size. They are grounded in order statistics theory and have a wide…
Polycrystalline metal failure often begins with stress concentration at grain boundaries. Identifying which microstructural features trigger these events is important but challenging because these extreme damage events are rare and the…
We study the statistics of the maximum and minimum of a set of $N$ random variables whose dynamical and statistical properties fall within the scope of infinite ergodic theory. These non-stationary yet recurrent systems are described, in…
We introduce the concept of geometric extremal graphical models, which are defined through the gauge function of the limit set obtained from suitably scaled random vectors in light-tailed margins. For block graphs, we prove results relating…
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…
Data-driven anomaly detection methods typically build a model for the normal behavior of the target system, and score each data instance with respect to this model. A threshold is invariably needed to identify data instances with high (or…
The univariate extreme value theory deals with the convergence in type of powers of elements of sequences of cumulative distribution functions on the real line when the power index gets infinite. In terms of convergence of random variables,…
We study extremal statistics and return intervals in stationary long-range correlated sequences for which the underlying probability density function is bounded and uniform. The extremal statistics we consider e.g., maximum relative to…
The modelling of multivariate extreme events is important in a wide variety of applications, including flood risk analysis, metocean engineering and financial modelling. A wide variety of statistical techniques have been proposed in the…
We investigate extreme value theory for physical systems with a global conservation law which describe renewal processes, mass transport models and long-range interacting spin models. As shown previously, a special feature is that the…
Extreme weather events have significant consequences, dominating the impact of climate on society. While high-resolution weather models can forecast many types of extreme events on synoptic timescales, long-term climatological risk…
Understanding and predicting uncertain things are the central themes of scientific evolution. Human beings revolve around these fears of uncertainties concerning various aspects like a global pandemic, health, finances, to name but a few.…
Using the superstatistics method, we propose an extension of the random matrix theory to cover systems with mixed regular-chaotic dynamics. Unlike most of the other works in this direction, the ensembles of the proposed approach are basis…
Factor models have large potencial in the modeling of several natural and human phenomena. In this paper we consider a multivariate time series $\mb{Y}_n$, ${n\geq 1}$, rescaled through random factors $\mb{T}_n$, ${n\geq 1}$, extending some…
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…
Extreme values geostatistics make it possible to model the asymptotic behaviors of random phenomena which depends on space or time parameters. In this paper, we propose new models of the extremal coefficient within a spatial stationary…
We generalize the concept of extremal index of a stationary random sequence to the series scheme of identically distributed random variables with random series sizes tending to infinity in probability. We introduce new extremal indices…
This paper develops new extremal principles of variational analysis that are motivated by applications to constrained problems of stochastic programming and semi-infinite programming without smoothness and/or convexity assumptions. These…
The object of this paper is twofold. From one side we study the dichotomy, in terms of the Extremal Index of the possible Extreme Value Laws, when the rare events are centred around periodic or non periodic points. Then we build a general…
Recent developments in extreme value statistics have established the so-called geometric approach as a powerful modelling tool for multivariate extremes. We tailor these methods to the case of spatial modelling and examine their efficacy at…