Article history: Received 14 November 2009 Received in revised form 29 April 2010 Accepted 6 May 2010

There are many reasons for the popular use of the isotropic or geometrically anisotropic covariance function and variogram in spatial statistics. A less known reason demonstrated in this paper is that an isotropic or geometrically anisotropic model would be the only choice in certain circumstances, for instance, when the underlying random field is smooth enough.

This paper proposes a new covariance matching based technique for blurred image PSF (point spread function) estimation. A patch based image degradation model is proposed for the covariance matching estimation framework. A robust covariance metric which is based on Riemannian manifold is adapted to measure the distance between covariance matrices. The optimal PSF is computed by minimizing the di...

We show that for the binomial process (or Bernoulli random walk) the orthogonal functionals constructed in Kroeker [14] for Markov chains can be expressed using the Krawtchouk polynomials, and by iterated stochastic integrals. This allows to construct a chaotic calculus based on gradient and divergence operators and structure equations, and to establish a Clark representation formula. As an app...

We propose a new measure of conditional dependence of random variables, based on normalized cross-covariance operators on reproducing kernel Hilbert spaces. Unlike previous kernel dependence measures, the proposed criterion does not depend on the choice of kernel in the limit of infinite data, for a wide class of kernels. At the same time, it has a straightforward empirical estimate with good c...

The subject is the overview of the use of quasi-entropy in finite dimensional spaces. Operator monotone functions and relative modular operators are used. The origin is the relative entropy, and the f -divergence, monotone metrics, covariance and the χ2-divergence are the most important particular cases. The extension of monotone metrics to those with two parameters is a new concept. Monotone m...

2. COMPARISON BETWEEN THE ECMWF 3DVAR AND 4DVAR SYSTEMS The ECMWF 4dVar system is, from the technical point of view, very similar to the 3dVar system. Both systems use the same unix scripts, and share much of the Fortran code. The same background error covariance matrix and observation operators are used, and most of the peripheral tasks such as fetching and archiving of fields and observations...

Three-dimensional bicovariant differential calculus on the quantum group SU q (2) is constructed using the approach based on global covariance under the action of the stabilizing subgroup U (1). Explicit representations of possible q-deformed Lie algebras are obtained in terms of differential operators. The consistent gauge covariant differential calculus on SU q (2) is uniquely defined. A non-...

Based on the Stein method and a general integration by parts framework we derive various bounds on the distance between probability measures. We show that this framework can be implemented on the Poisson space by covariance identities obtained from the Clark-Ocone representation formula and derivation operators. Our approach avoids the use of the inverse of the Ornstein-Uhlenbeck operator as in...