Related papers: Necessary and sufficient conditions for continuity…
We construct flexible likelihoods for multi-output Gaussian process models that leverage neural networks as components. We make use of sparse variational inference methods to enable scalable approximate inference for the resulting class of…
Random fields in nature often have, to a good approximation, Gaussian characteristics. For such fields, the relative densities of umbilical points -- topological defects which can be classified into three types -- have certain fixed values.…
We are studying stationary random processes with conditional polynomial moments that allow a continuous path modification. Processes with continuous path modification, are important because they are relatively easy to simulate. One does not…
We establish necessary and sufficient conditions for the existence of factorizable steady states of the Generalized Zero Range Process. This process allows transitions from a site $i$ to a site $i+q$ involving multiple particles with rates…
Gaussian Process Regression is a popular nonparametric regression method based on Bayesian principles that provides uncertainty estimates for its predictions. However, these estimates are of a Bayesian nature, whereas for some important…
Gaussian processes occupy one of the leading places in modern statistics and probability theory due to their importance and a wealth of strong results. The common use of Gaussian processes is in connection with problems related to…
.Stochastic models based on random diffusivities, such as the diffusing-diffusivity approach, are popular concepts for the description of non-Gaussian diffusion in heterogeneous media. Studies of these models typically focus on the moments…
We give an overview of the recent asymptotic results on the geometry of excursion sets of stationary random fields. Namely, we cover a number of limit theorems of central type for the volume of excursions of stationary (quasi--, positively…
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…
We consider a broad class of Continuous Time Random Walks with large fluctuations effects in space and time distributions: a random walk with trapping, describing subdiffusion in disordered and glassy materials, and a L\'evy walk process,…
This paper deals with the question of conditional sampling and prediction for the class of stationary max-stable processes which allow for a mixed moving maxima representation. We develop an exact procedure for conditional sampling using…
Covariance is a useful property for handling supergravity theories. In this paper, we prove a covariance property of supergravity field equations: under reasonable conditions, field equations of supergravity are covariant modulo other field…
On the lattice some of the salient features of pure gauge theories and of gauge theories with fermions in complex representations of the gauge group seem to be lost. These features can be recovered by considering part of the theory in the…
Gaussian Processes (GPs) has experienced tremendous success in geoscience in general and for bio-geophysical parameter retrieval in the last years. GPs constitute a solid Bayesian framework to formulate many function approximation problems…
In this article we give a general criterion for some dependent Gaussian models to belong to maximal domain of attraction of Gumbel, following an application of the Stein-Chen method studied in Arratia et al(1989). We also show the…
Gaussian processes are the gold standard for many real-world modeling problems, especially in cases where a model's success hinges upon its ability to faithfully represent predictive uncertainty. These problems typically exist as parts of…
Massive and massless Gaussian free fields can be described as generalized Gaussian processes indexed by an appropriate space of functions. In this article we study various approaches to approximate these fields and look at the fractal…
We study the representation of stationary Gaussian Markov random fields as factors of i.i.d. processes, with a focus on their approximation by finitely dependent distributions. Our model is a Gaussian field on $\mathbf{Z}^d$ such that the…
Motivated by objects such as electric fields or fluid streams, we study the problem of learning stochastic fields, i.e. stochastic processes whose samples are fields like those occurring in physics and engineering. Considering general…
Given a martingale sequence of random fields that satisfies a natural assumption of boundedness, it is shown that the pointwise limit of this sequence can be modified in such a way that a certain class of moduli of continuity is preserved.…