Related papers: Numerical Simulation of Non-Gaussian Random Fields…
Fourier methods are fundamental tools to analyze random fields. Statistical structures of homogeneous Gaussian random fields are completely characterized by the power spectrum. In non-Gaussian random fields, polyspectra, higher-order…
Gaussian random fields pervade all areas of science. However, it is often the departures from Gaussianity that carry the crucial signature of the nonlinear mechanisms at the heart of diverse phenomena, ranging from structure formation in…
Series expansions of isotropic Gaussian random fields on $\mathbb{S}^2$ with independent Gaussian coefficients and localized basis functions are constructed. Such representations with multilevel localised structure provide an alternative to…
Random fields are useful mathematical tools for representing natural phenomena with complex dependence structures in space and/or time. In particular, the Gaussian random field is commonly used due to its attractive properties and…
In (Hansen et al. 2002) we presented a new approach for measuring non-Gaussianity of the Cosmic Microwave Background (CMB) anisotropy pattern, based on the multivariate empirical distribution function of the spherical harmonics a_lm of a…
A problem of practical significance is the analysis of large, spatially distributed data sets. The problem is more challenging for variables that follow non-Gaussian distributions. We show that the spatial correlations between variables can…
A generator of spatio-temporal pseudo-random Gaussian fields that satisfy the "proportionality of scales" property (Tsyroulnikov, 2001) is presented. The generator is based on a third-order in time stochastic differential equation with a…
This paper presents a new numerical scheme for simulating stochastic processes specified by their marginal distribution functions and covariance functions. Stochastic samples are firstly generated to automatically satisfy target marginal…
A flexible model for non-stationary Gaussian random fields on hypersurfaces is introduced.The class of random fields on curves and surfaces is characterized by an amplitude spectral density of a second order elliptic differential…
We propose a method to probe higher-order correlators of the primordial density field through the inhomogeneity of local non-Gaussian parameters, such as f_NL, measured within smaller patches of the sky. Correlators between n-point…
We discuss the requirements of good statistics for quantifying non-Gaussianity in the Cosmic Microwave Background. The importance of rotational invariance and statistical independence is stressed, but we show that these are sometimes…
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…
We present an algorithm to identify sparse dependence structure in continuous and non-Gaussian probability distributions, given a corresponding set of data. The conditional independence structure of an arbitrary distribution can be…
Two algorithms are proposed to simulate space-time Gaussian random fields with a covariance function belonging to an extended Gneiting class, the definition of which depends on a completely monotone function associated with the spatial…
A semi-analytic method is proposed for the generation of realizations of a multivariate process of a given linear correlation structure and marginal distribution. This is an extension of a similar method for univariate processes,…
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…
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…
Galactic all-sky maps at very disparate frequencies, like in the radio and $\gamma$-ray regime, show similar morphological structures. This mutual information reflects the imprint of the various physical components of the interstellar…
Herein, we introduce and study a new class of discrete random fields designed for quick simulation and covariance inference under inhomogeneous condition. Simulation of these correlated fields can be done in a single pass instead of relying…
Generative modeling of spatio-temporal fields is crucial for a variety of applications, including stochastic weather generators and climate-model surrogates. However, many such fields exhibit complex dependence structures that vary across…