Related papers: Modeling spatial processes with unknown extremal d…
Generative models can be trained to emulate complex empirical data, but are they useful to make predictions in the context of previously unobserved environments? An intuitive idea to promote such extrapolation capabilities is to have the…
Extensive numerical evidence shows that the assimilation of observations has a stabilizing effect on unstable dynamics, in numerical weather prediction and elsewhere. In this paper, we apply mathematically rigorous methods to showing why…
Following our previous work on copula-based nonsymmetric dependence measures, we introduce similar measures for discrete random variables. The measures cover the range between two extremes: independence and complete dependence, which take…
We present a new asymptotic strategy for general micro-macro models which analyze complex viscoelastic fluids governed by coupled multiscale dynamics. In such models, the elastic stress appearing in the macroscopic continuum equation is…
This paper generalizes recent proposals of density forecasting models and it develops theory for this class of models. In density forecasting, the density of observations is estimated in regions where the density is not observed.…
Non-stationary extremal dependence, whereby the relationship between the extremes of multiple variables evolves over time, is commonly observed in many environmental and financial data sets. However, most multivariate extreme value models…
Estimation of stochastic processes evolving in a random environment is of crucial importance for example to predict aircraft trajectories evolving in an unknown atmosphere. For fixed parameter, interacting particle systems are a convenient…
Weak convergence of the empirical copula process is shown to hold under the assumption that the first-order partial derivatives of the copula exist and are continuous on certain subsets of the unit hypercube. The assumption is…
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…
This paper investigates the modeling of an important class of degradation data, which are collected from a spatial domain over time; for example, the surface quality degradation. Like many existing time-dependent stochastic degradation…
The empirical copula process plays a central role in the asymptotic analysis of many statistical procedures which are based on copulas or ranks. Among other applications, results regarding its weak convergence can be used to develop…
We propose a series-based nonparametric specification test for a regression function when data are spatially dependent, the `space' being of a general economic or social nature. Dependence can be parametric, parametric with increasing…
The angular measure on the unit sphere characterizes the first-order dependence structure of the components of a random vector in extreme regions and is defined in terms of standardized margins. Its statistical recovery is an important step…
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…
We propose dynamical collapse models in which the stochastic collapse terms affect only photons and/or gravitons. In principle, isolated systems comprising only massive particles could evolve unitarily indefinitely in such models. In…
There has been a growing interest in providing models for multivariate spatial processes. A majority of these models specify a parametric matrix covariance function. Based on observations, the parameters are estimated by maximum likelihood…
We introduce a flexible and scalable class of Bayesian geostatistical models for discrete data, based on the class of nearest neighbor mixture transition distribution processes (NNMP), referred to as discrete NNMP. The proposed class…
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…
Modelling of precipitation and its extremes is important for urban and agriculture planning purposes. We present a method for producing spatial predictions and measures of uncertainty for spatio-temporal data that is heavy-tailed and…
In environmental science applications, extreme events frequently exhibit a complex spatio-temporal structure, which is difficult to describe flexibly and estimate in a computationally efficient way using state-of-art parametric…