Related papers: Asymmetric Matrix-Valued Covariances for Multivari…

The prevalence of multivariate space-time data collected from monitoring networks and satellites, or generated from numerical models, has brought much attention to multivariate spatio-temporal statistical models, where the covariance…

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…

Designing a covariance function that represents the underlying correlation is a crucial step in modeling complex natural systems, such as climate models. Geospatial datasets at a global scale usually suffer from non-stationarity and…

Cokriging is the common method of spatial interpolation (best linear unbiased prediction) in multivariate geostatistics. While best linear prediction has been well understood in univariate spatial statistics, the literature for the…

This article explores the optimization of variational approximations for posterior covariances of Gaussian multiway arrays. To achieve this, we establish a natural differential geometric optimization framework on the space using the…

There has been a growing interest in providing models for multivariate spatial processes. A majority of these models specify a parametric matrix covariance function. Based on observations, the parameters are estimated by maximum likelihood…

Statistical modeling of spatiotemporal phenomena often requires selecting a covariance matrix from a covariance class. Yet standard parametric covariance families can be insufficiently flexible for practical applications, while…

Functions which are covariant or invariant under the transformations of a compact linear group $G$ acting in a euclidean space $\real^n$, can be profitably studied as functions defined in the orbit space of the group. The orbit space is the…

Data augmentation in feature space is effective to increase data diversity. Previous methods assume that different classes have the same covariance in their feature distributions. Thus, feature transform between different classes is…

Relying on recent advances in statistical estimation of covariance distances based on random matrix theory, this article proposes an improved covariance and precision matrix estimation for a wide family of metrics. The method is shown to…

Random fields on the sphere play a fundamental role in the natural sciences. This paper presents a simulation algorithm parenthetical to the spectral turning bands method used in Euclidean spaces, for simulating scalar- or vector-valued…

Covariance representations are developed for the uniform distributions on the Euclidean spheres in terms of spherical gradients and Hessians. They are applied to derive a number of Sobolev type inequalities and to recover and refine the…

Spatial models for areal data are often constructed such that all pairs of adjacent regions are assumed to have near-identical spatial autocorrelation. In practice, data can exhibit dependence structures more complicated than can be…

This paper studies Gaussian random fields with Mat\'ern covariance functions with smooth parameter $\nu>2$. Two cases of parameter spaces, the Euclidean space and $N$-dimensional sphere, are considered. For such smooth Gaussian fields, we…

Spherical regression explores relationships between variables on spherical domains. We develop a nonparametric model that uses a diffeomorphic map from a sphere to itself. The restriction of this mapping to diffeomorphisms is natural in…

The presented paper is devoted to statistical modeling of Gaussian scalar real random fields inside a three-dimensional sphere (ball). We propose a statistical model describing the spatial heterogeneity in a unit ball and a numerical…

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…

The spatial random-effects model is flexible in modeling spatial covariance functions, and is computationally efficient for spatial prediction via fixed rank kriging. However, the success of this model depends on an appropriate set of basis…

With the advent of wide-spread global and continental-scale spatiotemporal datasets, increased attention has been given to covariance functions on spheres over time. This paper provides results for stationary covariance functions of random…

Spherically embedded spatial data are spatially indexed observations whose values naturally reside on or can be equivalently mapped to the unit sphere. Such data are increasingly ubiquitous in fields ranging from geochemistry to demography.…