Related papers: How to model the covariance structure in a spatial…

Geographical data are generally autocorrelated. In this case, it is preferable to select spread units. In this paper, we propose a new method for selecting well-spread samples from a finite spatial population with equal or unequal inclusion…

Parametric distributions are an important part of statistics. There is now a voluminous literature on different fascinating formulations of flexible distributions. We present a selective and brief overview of a small subset of these…

The theory of Gaussian quantum fluctuations around classical steady states in nonlinear quantum-optical systems (also known as standard linearization) is a cornerstone for the analysis of such systems. Its simplicity, together with its…

Estimation of the mean vector and covariance matrix is of central importance in the analysis of multivariate data. In the framework of generalized linear models, usually the variances are certain functions of the means with the normal…

This paper presents a theory for how geometric image transformations can be handled by a first layer of linear receptive fields, in terms of true covariance properties, which, in turn, enable geometric invariance properties at higher levels…

Coarse-grained descriptions of dislocation motion in crystalline metals inherently represent a loss of information regarding dislocation-dislocation interactions. In the present work, we consider a coarse-graining framework capable of…

Standard geostatistical models assume second order stationarity of the underlying Random Function. In some instances, there is little reason to expect the spatial dependence structure to be stationary over the whole region of interest. In…

Geophysical and other natural processes often exhibit non-stationary covariances and this feature is important to take into account for statistical models that attempt to emulate the physical process. A convolution-based model is used to…

We review the status of our understanding of nucleon structure based on the modelling of different kinds of parton distributions. We use the concept of generalized transverse momentum dependent parton distributions and Wigner distributions,…

We analyse the covariance of the one-dimensional mass power spectrum along lines of sight. The covariance reveals the correlation between different modes of fluctuations in the cosmic density field and gives the sample variance error for…

Estimation of the covariance structure of spatial processes is of fundamental importance in spatial statistics. In the literature, several non-parametric and semi-parametric methods have been developed to estimate the covariance structure…

Spatial transcriptomics measures the expression of thousands of genes in a tissue sample while preserving its spatial structure. This class of technologies has enabled the investigation of the spatial variation of gene expressions and their…

Several statistical models used in genome-wide prediction assume independence of marker allele substitution effects, but it is known that these effects might be correlated. In statistics, graphical models have been identified as a useful…

Large-scale Gaussian process inference has long faced practical challenges due to time and space complexity that is superlinear in dataset size. While sparse variational Gaussian process models are capable of learning from large-scale data,…

This work addresses the interpolation of probability measures within a spatial statistics framework. We develop a Kriging approach in the Wasserstein space, leveraging the quantile function representation of the one-dimensional Wasserstein…

Covariance matrices of random vectors contain information that is crucial for modelling. Specific structures and patterns of the covariances (or correlations) may be used to justify parametric models, e.g., autoregressive models. Until now,…

Undirected graphs are often used to describe high dimensional distributions. Under sparsity conditions, the graph can be estimated using $\ell_1$-penalization methods. We propose and study the following method. We combine a multiple…

Gaussian double Markovian models consist of covariance matrices constrained by a pair of graphs specifying zeros simultaneously in the covariance matrix and its inverse. We study the semi-algebraic geometry of these models, in particular…

This paper presents a general form of the covariance matrix structure for a vector random field that is axially symmetric and mean square continuous on the sphere and provides a series representation for a longitudinally reversible one. The…

Traditional spatio-temporal models for areal data typically begin with spatial structure imposed at the level of random effects and later extend to include temporal dynamics. We propose an alternative hierarchical modeling framework that…