Related papers: Non-Stationary Dependence Structures for Spatial E…
The max-stable process is an asymptotically justified model for spatial extremes. In particular, we focus on the hierarchical extreme-value process (HEVP), which is a particular max-stable process that is conducive to Bayesian computing.…
Currently available models for spatial extremes suffer either from inflexibility in the dependence structures that they can capture, lack of scalability to high dimensions, or in most cases, both of these. We present an approach to spatial…
The conditional extremes framework allows for event-based stochastic modeling of dependent extremes, and has recently been extended to spatial and spatio-temporal settings. After standardizing the marginal distributions and applying an…
Statistical modeling of multivariate and spatial extreme events has attracted broad attention in various areas of science. Max-stable distributions and processes are the natural class of models for this purpose, and many parametric families…
Nonstationarity is a major challenge in analyzing spatial data. For example, daily precipitation measurements may have increased variability and decreased spatial smoothness in areas with high mean rainfall. Common nonstationary covariance…
With the proliferation of modern high-resolution measuring instruments mounted on satellites, planes, ground-based vehicles and monitoring stations, a need has arisen for statistical methods suitable for the analysis of large spatial…
Understanding and predicting environmental phenomena often requires the construction of spatio-temporal statistical models, which are typically Gaussian processes. A common assumption made on Gaussian processes is that of covariance…
The statistical theory of extremes is extended to observations that are non-stationary and not independent. The non-stationarity over time and space is controlled via the scedasis (tail scale) in the marginal distributions. Spatial…
Nonstationary Gaussian process models can capture complex spatially varying dependence structures in spatial datasets. However, the large number of observations in modern datasets makes fitting such models computationally intractable with…
Let $X_{i,n},n\in \mathbb{N},1\leq i\leq n$, be a triangular array of independent $\mathbb{R}^d$-valued Gaussian random vectors with correlation matrices $\Sigma_{i,n}$. We give necessary conditions under which the row-wise maxima converge…
Parametric inference for spatial max-stable processes is difficult since the related likelihoods are unavailable. A composite likelihood approach based on the bivariate distribution of block maxima has been recently proposed in the…
Many environmental processes exhibit weakening spatial dependence as events become more extreme. Well-known limiting models, such as max-stable or generalized Pareto processes, cannot capture this, which can lead to a preference for models…
Extremal graphical models are sparse statistical models for multivariate extreme events. The underlying graph encodes conditional independencies and enables a visual interpretation of the complex extremal dependence structure. For the…
Max-stable processes are a popular tool for the study of environmental extremes, and the extremal skew-$t$ process is a general model that allows for a flexible extremal dependence structure. For inference on max-stable processes with…
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…
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…
We propose a vector generalized additive modeling framework for taking into account the effect of covariates on angular density functions in a multivariate extreme value context. The proposed methods are tailored for settings where the…
Max-stable random fields provide canonical models for the dependence of multivariate extremes. Inference with such models has been challenging due to the lack of tractable likelihoods. In contrast, the finite dimensional cumulative…
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…
Estimation of stationary dependence structure parameters using only a single realisation of the spatial process, typically leads to inaccurate estimates and poorly identified parameters. A common way to handle this is to fix some of the…