Related papers: Simulation of Gaussian random field in a ball
Spherical regression, in which both covariates and responses lie on the sphere, arises in many scientific applications and has attracted considerable methodological attention in recent years. Despite this progress, constructing flexible and…
A novel random field model or the reconstruction of turbulent velocity fluctuations from inhomogeneous characteristic flow quantities in terms of stochastic Fourier-type integrals has recently been introduced and analyzed by the authors.…
The use of statistical modeling in baseball has received substantial attention recently in both the media and academic community. We focus on a relatively under-explored topic: the use of statistical models for the analysis of fielding…
Modeling data with non-stationary covariance structure is important to represent heterogeneity in geophysical and other environmental spatial processes. In this work, we investigate a multistage approach to modeling non-stationary…
Dense 3D representations of the environment have been a long-term goal in the robotics field. While previous Neural Radiance Fields (NeRF) representation have been prevalent for its implicit, coordinate-based model, the recent emergence of…
This is an experimental case study in real algebraic geometry, aimed at computing the image of a semialgebraic subset of 3-space under a polynomial map into the plane. For general instances, the boundary of the image is given by two highly…
Recent models for discrete euclidean quantum gravity incorporate a sum over simplicial triangulations. We describe an algorithm for simulating such models in general dimensions. As illustration we show results from simulations in four…
This chapter discusses the importance of incorporating three-dimensional symmetries in the context of statistical learning models geared towards the interpolation of the tensorial properties of atomic-scale structures. We focus on Gaussian…
The quantum fluctuations of fields can exhibit subtle correlations in space and time. As the interval between a pair of measurements varies, the correlation function can change sign, signaling a shift between correlation and…
The R\'enyi function plays an important role in the analysis of multifractal random fields. For random fields on the sphere, there are three models in the literature where the R\'enyi function is known explicitly. The theoretical part of…
This paper deals with the spectral element modeling of seismic wave propagation at the global scale. Two aspects relevant to low-frequency studies are particularly emphasized. First, the method is generalized beyond the Cowling…
This survey is devoted to recent developments in the statistical analysis of spherical data, with a view to applications in Cosmology. We will start from a brief discussion of Cosmological questions and motivations, arguing that most…
Starting from the observation of an R^n-Gaussian vector of mean f and covariance matrix \sigma^2 I_n (I_n is the identity matrix), we propose a method for building a Euclidean confidence ball around f, with prescribed probability of…
Current statistics literature on statistical inference of random fields typically assumes that the fields are stationary or focuses on models of non-stationary Gaussian fields with parametric/semiparametric covariance families, which may…
Stochastic and conditional simulation methods have been effective towards producing realistic realizations and simulations of spatial numerical models that share equal probability of occurrence. Application of these methods are valuable…
We construct time dependent random fields on the sphere through coordinates change and subordination and we study the associated angular power spectrum. Some of this random fields arise naturally as solutions of partial differential…
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…
We discuss D-dimensional scalar field interacting with a scale invariant random metric which is either a Gaussian field or a square of a Gaussian field. The metric depends on d-dimensional coordinates (where d is less than D). By a…
Gaussian process is a theoretically appealing model for nonparametric analysis, but its computational cumbersomeness hinders its use in large scale and the existing reduced-rank solutions are usually heuristic. In this work, we propose a…
We provide a new approach, along with extensions, to results in two important papers of Worsley, Siegmund and coworkers closely tied to the statistical analysis of fMRI (functional magnetic resonance imaging) brain data. These papers…