We begin with isotropic Gaussian random fields, and show how the Bochner–Godement theorem gives a natural way to describe their covariance structure. continue study of Matérn processes on Euclidean space, spheres, manifolds graphs, using Bessel potentials stochastic partial differential equations (SPDEs). then turn from this continuous setting approximating discrete settings, Markov fields (GMR...

The covariance of a stationary process X is diagonalized by Fourier transform. It does not take into account the complex phase and defines Gaussian maximum entropy models. We introduce general family harmonic moments, which rely on phases to capture non-Gaussian properties. They are defined as Hˆ(LX), where L linear operator Hˆ non-linear multiplies each coefficient integers. can also be calcul...

A multivariate ensemble Kalman filter (MvEnKF) implemented on a massively parallel computer architecture has been developed for the Poseidon ocean circulation model and tested with a Pacific basin model configuration. There are about 2 million prognostic state-vector variables. Parallelism for the data assimilation step is achieved by regionalization of the background-error covariances that are...

One crucial feature of zygotic linkage disequilibrium (LD) analysis is its direct use of diploid genotyping data, irrespective of the type of mating system. Previous theories from an evolutionary perspective mainly focus on gametic LD, but the equivalent development for zygotic LD is not available. Here I study the evolution of zygotic LD and the covariances between gametic and zygotic LDs or b...

This paper presents a parametric family of compactly-supported positive semidefinite kernels aimed to model the covariance structure second-order stationary isotropic random fields defined in d-dimensional Euclidean space. Both and its spectral density have an analytic expression involving hypergeometric functions $${}_2F_1$$ $${}_1F_2$$ , respectively, four real-valued parameters related corre...

We consider the problem of jointly estimating multiple related zero-mean Gaussian distributions from data. propose to estimate these covariance matrices using Laplacian regularized stratified model fitting, which includes loss and regularization terms for each matrix, also a term that encourages different covariances be close. This method ‘borrows strength’ neighboring covariances, improve its ...

This paper presents a novel algorithm for nding the solution of the generalized eigenproblem where the matrices involved contain expectation values from stochastic processes. The algorithm is iterative and sequential to its structure and uses on-line stochastic approximation to reach an equilibrium point. A quotient between two quadratic forms is suggested as an energy function for this problem...