Related papers: Statistical inference for max-stable processes in …
This paper gives a new representation of Pickands' constants, which arise in the study of extremes for a variety of Gaussian processes. Using this representation, we resolve the long-standing problem of devising a reliable algorithm for…
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…
This article investigates the phenomenon of maximal rigidity in spatial processes, where perfect interpolation of the process is possible from partial information, specifically, from its restriction to a strict subdomain, often resulting in…
In this paper we concentrate on an alternative modeling strategy for positive data that exhibit spatial or spatio-temporal dependence. Specifically we propose to consider stochastic processes obtained trough a monotone transformation of…
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…
With any max-stable random process $\eta$ on $\mathcal{X}=\mathbb{Z}^d$ or $\mathbb{R}^d$, we associate a random tessellation of the parameter space $\mathcal{X}$. The construction relies on the Poisson point process representation of the…
This paper is concerned with statistical inference for infinite range interaction Gibbs point processes and in particular for the large class of Ruelle superstable and lower regular pairwise interaction models. We extend classical…
Stochastic Spatio-Temporal processes are prevalent across domains ranging from modeling of plasma to the turbulence in fluids to the wave function of quantum systems. This letter studies a measure-theoretic description of such systems by…
A method for sequential Bayesian inference of the static parameters of a dynamic state space model is proposed. The method is based on the observation that many dynamic state space models have a relatively small number of static parameters…
Multistable processes, that is, processes which are, at each "time", tangent to a stable process, but where the index of stability varies along the path, have been recently introduced as models for phenomena where the intensity of jumps is…
In this paper, we study the asymptotic relation between the maximum of acontinuous order statistics process formed by stationary Gaussian processesand the maximum of this process sampled at discrete time points. It is shown that, these two…
A key challenge in spatial statistics is the analysis for massive spatially-referenced data sets. Such analyses often proceed from Gaussian process specifications that can produce rich and robust inference, but involve dense covariance…
Gaussian processes are a powerful class of non-linear models, but have limited applicability for larger datasets due to their high computational complexity. In such cases, approximate methods are required, for example, the recently…
We introduce fully scalable Gaussian processes, an implementation scheme that tackles the problem of treating a high number of training instances together with high dimensional input data. Our key idea is a representation trick over the…
Various approaches to stochastic processes exist, noting that key properties such as measurability and continuity are not trivially satisfied. We introduce a new theory for Gaussian processes using improper linear functionals. Using a…
In order to describe the extremal behaviour of some stochastic process $X$, approaches from univariate extreme value theory are typically generalized to the spatial domain. In particular, generalized peaks-over-threshold approaches allow…
We consider a one-dimensional stationary stochastic process $x(\tau)$ of duration $T$. We study the probability density function (PDF) $P(t_{\rm m}|T)$ of the time $t_{\rm m}$ at which $x(\tau)$ reaches its global maximum. By using a path…
Maximizing the likelihood has been widely used for estimating the unknown covariance parameters of spatial Gaussian processes. However, evaluating and optimizing the likelihood function can be computationally intractable, particularly for…
In this paper, we consider isotropic and stationary max-stable, inverse max-stable and max-mixture processes $X=(X(s))\_{s\in\bR^2}$ and the damage function $\cD\_X^{\nu}= |X|^\nu$ with $0<\nu<1/2$. We study the quantitative behavior of a…
The linear fractional stable motion generalizes two prominent classes of stochastic processes, namely stable L\'evy processes, and fractional Brownian motion. For this reason it may be regarded as a basic building block for continuous time…