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Spatially isotropic max-stable processes have been used to model extreme spatial or space-time observations. One prominent model is the Brown-Resnick process, which has been successfully fitted to time series, spatial data and space-time…
Predicting extreme events is important in many applications in risk analysis. The extreme-value theory suggests modelling extremes by max-stable distributions. The Bayesian approach provides a natural framework for statistical prediction.…
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…
In multivariate or spatial extremes, inference for max-stable processes observed at a large collection of locations is among the most challenging problems in computational statistics, and current approaches typically rely on less expensive…
In the paper we consider higher-order partial differential equations from the class of linear dispersive equations. We investigate solutions to these equations subject to random initial conditions given by harmonizable…
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…
Max-stable processes have proved to be useful for the statistical modelling of spatial extremes. Several representations of max-stable random fields have been proposed in the literature. For statistical inference it is often assumed that…
Statistical modelling of spatial extreme events has gained increasing attention over the last few decades with max-stable processes, and more recently $r$-Pareto processes, becoming the reference tools for the statistical analysis of…
In this paper, we consider a stochastic system described by a differential equation admitting a spatially varying random coefficient. The differential equation has been employed to model various static physics systems such as elastic…
Regularly varying stochastic processes are able to model extremal dependence between process values at locations in random fields. We investigate the empirical extremogram as an estimator of dependence in the extremes. We provide conditions…
Max-stable processes are a common choice for modelling spatial extreme data as they arise naturally as the infinite-dimensional generalisation of multivariate extreme value theory. Statistical inference for such models is complicated by the…
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…
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…
Analysis of extremal behavior of stochastic processes is a key ingredient in a wide variety of applications, including probability, statistical physics, theoretical computer science, and learning theory. In this paper, we consider centered…
Regularly varying stochastic processes model extreme dependence between process values at different locations and/or time points. For such processes we propose a two-step parameter estimation of the extremogram, when some part of the domain…
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…
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…
Max-stable distributions and processes are important models for extreme events and the assessment of tail risks. The full, multivariate likelihood of a parametric max-stable distribution is complicated and only recent advances enable its…
We consider Ising mixed $p$-spin glasses at high-temperature and without external field, and study the problem of sampling from the Gibbs distribution $\mu$ in polynomial time. We develop a new sampling algorithm with complexity of the same…
Conditional density estimation (density regression) estimates the distribution of a response variable y conditional on covariates x. Utilizing a partition model framework, a conditional density estimation method is proposed using logistic…