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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…
Modern methods for quantifying and predicting species distribution play a crucial part in biodiversity conservation. Occupancy models are a popular choice for analyzing species occurrence data as they allow to separate the observational…
Extreme events over large spatial domains may exhibit highly heterogeneous tail dependence characteristics, yet most existing spatial extremes models yield only one dependence class over the entire spatial domain. To accurately characterize…
Max-stable processes are natural models for spatial extremes because they provide suitable asymptotic approximations to the distribution of maxima of random fields. In the recent past, several parametric families of stationary max-stable…
The classical modeling of spatial extremes relies on asymptotic models (i.e., max-stable processes or $r$-Pareto processes) for block maxima or peaks over high thresholds, respectively. However, at finite levels, empirical evidence often…
Bayesian hierarchical models with latent Gaussian layers have proven very flexible in capturing complex stochastic behavior and hierarchical structures in high-dimensional spatial and spatio-temporal data. Whereas simulation-based Bayesian…
Statistical modeling of a nonstationary spatial extremal dependence structure is challenging. Max-stable processes are common choices for modeling spatially-indexed block maxima, where an assumption of stationarity is usual to make…
Data derived from remote sensing or numerical simulations often have a regular gridded structure and are large in volume, making it challenging to find accurate spatial models that can fill in missing grid cells or simulate the process…
This work has been motivated by the challenge of the 2017 conference on Extreme-Value Analysis (EVA2017), with the goal of predicting daily precipitation quantiles at the $99.8\%$ level for each month at observed and unobserved locations.…
Modeling the joint distribution of extreme weather events in multiple locations is a challenging task with important applications. In this study, we use max-stable models to study extreme daily precipitation events in Switzerland. The…
Max-stable processes are increasingly widely used for modelling complex extreme events, but existing fitting methods are computationally demanding, limiting applications to a few dozen variables. $r$-Pareto processes are mathematically…
With extreme weather events becoming more common, the risk posed by surface water flooding is ever increasing. In this work we propose a model, and associated Bayesian inference scheme, for generating probabilistic (high-resolution…
The areal modeling of the extremes of a natural process such as rainfall or temperature is important in environmental statistics; for example, understanding extreme areal rainfall is crucial in flood protection. This article reviews recent…
Various natural phenomena exhibit spatial extremal dependence at short spatial distances. However, existing models proposed in the spatial extremes literature often assume that extremal dependence persists across the entire domain. This is…
In this chapter, we show how to efficiently model high-dimensional extreme peaks-over-threshold events over space in complex non-stationary settings, using extended latent Gaussian Models (LGMs), and how to exploit the fitted model in…
Modelling the extremal dependence structure of spatial data is considerably easier if that structure is stationary. However, for data observed over large or complicated domains, non-stationarity will often prevail. Current methods for…
With continued advances in Geographic Information Systems and related computational technologies, statisticians are often required to analyze very large spatial datasets. This has generated substantial interest over the last decade, already…
The spatial modeling of extreme snow is important for adequate risk management in Alpine and high altitude countries. A natural approach to such modeling is through the theory of max-stable processes, an infinite-dimensional extension of…
High dimensional space-time data pose known computational challenges when fitting spatio-temporal models. Such data show dependence across several dimensions of space as well as in time, and can easily involve hundreds of thousands of…
Precipitation exceedance probabilities are widely used in engineering design, risk assessment, and floodplain management. While common approaches like NOAA Atlas 14 assume that extreme precipitation characteristics are stationary over time,…