Related papers: On the Local Structure and Approximation Stability…
This work addresses the problem of simulating Gaussian random fields that are continuously indexed over a class of metric graphs, termed graphs with Euclidean edges, being more general and flexible than linear networks. We introduce three…
A non-stationary spatial Gaussian random field (GRF) is described as the solution of an inhomogeneous stochastic partial differential equation (SPDE), where the covariance structure of the GRF is controlled by the coefficients in the SPDE.…
Convex regularization techniques are now widespread tools for solving inverse problems in a variety of different frameworks. In some cases, the functions to be reconstructed are naturally viewed as realizations from random processes; an…
Many applications of Gaussian random fields and Gaussian random processes are limited by the computational complexity of evaluating the probability density function, which involves inverting the relevant covariance matrix. In this work, we…
This paper investigates the approximation of Gaussian random variables in Banach spaces, focusing on the high-probability bounds for the approximation of Gaussian random variables using finitely many observations. We derive non-asymptotic…
Covariance parameter estimation of Gaussian processes is analyzed in an asymptotic framework. The spatial sampling is a randomly perturbed regular grid and its deviation from the perfect regular grid is controlled by a single scalar…
We provide a method for fast and exact simulation of Gaussian random fields on spheres having isotropic covariance functions. The method proposed is then extended to Gaussian random fields defined over spheres cross time and having…
The paper deals with multivariate Gaussian random fields defined over generalized product spaces that involve the hypertorus. The assumption of Gaussianity implies the finite dimensional distributions to be completely specified by the…
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…
This paper investigates Gaussian Markov random field approximations to nonstationary Gaussian fields using graph representations of stochastic partial differential equations. We establish approximation error guarantees building on the…
We introduce a simple representation for isotropic spherical random fields and we discuss how it allows to discuss different notions of sparsity under isotropy. We also show how a suitable construction of sparse fields can mimic well the…
This paper presents a new approach to the estimation of the deformation of an isotropic Gaussian random field on $\mathbb{R}^2$ based on dense observations of a single realization of the deformed random field. Under this framework we…
We obtain formulae for the expected number and height distribution of critical points of smooth isotropic Gaussian random fields parameterized on Euclidean space or spheres of arbitrary dimension. The results hold in general in the sense…
In this paper, we attempt to shed light on a new class of nonstationary random fields which exhibit, what we call, local invariant nonstationarity. We argue that the local invariant property has a special interaction with a new generalized…
We develop an operator-theoretic framework for stability and statistical concentration in nonlinear inverse problems with block-structured parameters. Under a unified set of assumptions combining blockwise Lipschitz geometry, local…
Isotropic $\alpha$-stable distributions are central in the theory of heavy-tailed distributions and play a role similar to that of the Gaussian density among finite second-moment laws. Given a sequence of $n$ observations, we are interested…
We prove Central Limit Theorems and Stein-like bounds for the asymptotic behaviour of nonlinear functionals of spherical Gaussian eigenfunctions. Our investigation combine asymptotic analysis of higher order moments for Legendre polynomials…
In this paper we define (empirical) quadratic variations for a Gaussian isotropic random field $f$ on a unit sphere as sums over equidistant increments on one single geodesic line on the surface of the sphere. We prove a noncentral limit…
Generating large-scale samples of stationary random fields is of great importance in the fields such as geomaterial modeling and uncertainty quantification. Traditional methodologies based on covariance matrix decomposition have the…
We study how sampling geometry contributes to uncertainty in modeling spatial geophysical observations as sampled random fields characterized by stationary, isotropic, parametric covariance functions. We incorporate the signature of…