Related papers: Advances in Statistical Modeling of Spatial Extrem…
To mitigate the risk posed by extreme rainfall events, we require statistical models that reliably capture extremes in continuous space with dependence. However, assuming a stationary dependence structure in such models is often erroneous,…
The extremal behaviour of a Markov chain is typically characterized by its tail chain. For asymptotically dependent Markov chains existing formulations fail to capture the full evolution of the extreme event when the chain moves out of the…
In this work, we develop a constructive modeling framework for extreme threshold exceedances in repeated observations of spatial fields, based on general product mixtures of random fields possessing light or heavy-tailed margins and various…
Extremes occur in stationary regularly varying time series as short periods with several large observations, known as extremal blocks. We study cluster statistics summarizing the behavior of functions acting on these extremal blocks.…
Spatial maps of extreme precipitation are crucial in flood protection. With the aim of producing maps of precipitation return levels, we propose a novel approach to model a collection of spatially distributed time series where the…
The study of multivariate extremes is dominated by multivariate regular variation, although it is well known that this approach does not provide adequate distinction between random vectors whose components are not always simultaneously…
Conditional independence, graphical models and sparsity are key notions for parsimonious statistical models and for understanding the structural relationships in the data. The theory of multivariate and spatial extremes describes the risk…
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…
This paper introduces a novel measure to quantify the directional dependence of extreme events between two variables. The proposed approach is designed to capture asymmetric tail dependence by studying conditional tail expectations of…
We introduce a new formulation of structural causal models for extremes, called the extremal structural causal model (eSCM). Unlike conventional structural causal models, where randomness is governed by a probability distribution, eSCMs use…
Many environmental processes such as rainfall, wind or snowfall are inherently spatial and the modelling of extremes has to take into account that feature. In addition, environmental processes are often attached with an angle, e.g., wind…
We consider the clustering of extremes for stationary regularly varying random fields over arbitrary growing index sets. We study sufficient assumptions on the index set such that the limit of the point random fields of the exceedances…
We study the spatio-temporal features of extremal sub-daily precipitation data over the Piave river basin in northeast Italy using a rich database of observed hourly rainfall. Empirical evidence suggests that both the marginal and…
Being the max-analogue of $\alpha$-stable stochastic processes, max-stable processes form one of the fundamental classes of stochastic processes. With the arrival of sufficient computational capabilities, they have become a benchmark in the…
This paper introduces a class of copula models for spatial data, based on multivariate Pareto-mixture distributions. We explore the tail properties of these models, demonstrating their ability to capture both tail dependence and asymptotic…
Extreme value theory provides an asymptotically justified framework for estimation of exceedance probabilities in regions where few or no observations are available. For multivariate tail estimation, the strength of extremal dependence is…
We introduce the extremal range, a local statistic for studying the spatial extent of extreme events in random fields on $\mathbb{R}^d$. Conditioned on exceedance of a high threshold at a location $s$, the extremal range at $s$ is the…
The extremes of a stationary time series typically occur in clusters. A primary measure for this phenomenon is the extremal index, representing the reciprocal of the expected cluster size. Both a disjoint and a sliding blocks estimator for…
The classical multivariate extreme-value theory concerns the modeling of extremes in a multivariate random sample, suggesting the use of max-stable distributions. In this work, the classical theory is extended to the case where aggregated…
Natural disasters may have considerable impact on society as well as on (re)insurance industry. Max-stable processes are ideally suited for the modeling of the spatial extent of such extreme events, but it is often assumed that there is no…