Related papers: High-dimensional peaks-over-threshold inference
Designs conditions for marine structures are typically informed by threshold-based extreme value analyses of oceanographic variables, in which excesses of a high threshold are modelled by a generalized Pareto (GP) distribution. Too low a…
The coarse spatial resolution of gridded climate models, such as general circulation models, limits their direct use in projecting socially relevant variables like extreme precipitation. Most downscaling methods estimate the conditional…
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…
The extreme value dependence of regularly varying stationary time series can be described by the spectral tail process. Drees, Segers and Warchol [Extremes 18(3): 369--402, 2015] proposed estimators of the marginal distributions of this…
Max-stable processes are the natural analogues of the generalized extreme-value distribution for the modelling of extreme events in space and time. Under suitable conditions, these processes are asymptotically justified models for maxima of…
In most risk assessment studies, it is important to accurately capture the entire distribution of the multivariate random vector of interest from low to high values. For example, in climate sciences, low precipitation events may lead to…
Max-stable processes are the natural extension of the classical extreme-value distributions to the functional setting, and they are increasingly widely used to estimate probabilities of complex extreme events. In this paper we broaden them…
Complex computer codes or models can often be run in a hierarchy of different levels of complexity ranging from the very basic to the sophisticated. The top levels in this hierarchy are typically expensive to run, which limits the number of…
Extreme value theory offers a statistical framework for quantifying the risk of rare events, with the generalized Pareto (GP) distribution providing the canonical limit model for univariate threshold exceedances. In many applications,…
Modelling and forecasting the occurrence of extreme events is especially difficult when the event process is nonstationary, with changes in both the rate at which extremes occur and the magnitude of the extremes when they occur. We approach…
We review some recent development in the theory of spatial extremes related to Pareto Processes and modeling of threshold exceedances. We provide theoretical background, methodology for modeling, simulation and inference as well as an…
Intense precipitation events are commonly known to be associated with an increased risk of flooding. As a result of the societal and infrastructural risks linked with flooding, extremes of precipitation require careful modelling. Extreme…
In extreme value analysis, sensitivity of inference to the definition of extreme event is a paramount issue. Under the peaks-over-threshold (POT) approach, this translates directly into the need of fitting a Generalized Pareto distribution…
Quantifying changes in the probability and magnitude of extreme flooding events is key to mitigating their impacts. While hydrodynamic data are inherently spatially dependent, traditional spatial models such as Gaussian processes are poorly…
Gaussian processes (GPs) are a powerful tool for probabilistic inference over functions. They have been applied to both regression and non-linear dimensionality reduction, and offer desirable properties such as uncertainty estimates,…
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…
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…
The most popular approach in extreme value statistics is the modelling of threshold exceedances using the asymptotically motivated generalised Pareto distribution. This approach involves the selection of a high threshold above which the…
This paper provides the basis for new methods of inference for max-stable processes \xi\ on general spaces that admit a certain incremental representation, which, in important cases, has a much simpler structure than the max-stable process…
Environmental data science for spatial extremes has traditionally relied heavily on max-stable processes. Even though the popularity of these models has perhaps peaked with statisticians, they are still perceived and considered as the…