Numerical Aspects of the Application of Recursive Filters to Variational Statistical Analysis. Part II: Spatially Inhomogeneous and Anisotropic General Covariances

Purser, R. James; Wu, Wan-Shu; Parrish, David F.; Roberts, Nigel M.
August 2003
Monthly Weather Review;Aug2003 Parts 1 and 2, Vol. 131 Issue 8, p1536
Academic Journal
In this second part of a two-part study of recursive filter techniques applied to the synthesis of covariances in a variational analysis, methods by which non-Gaussian shapes and spatial inhomogeneities and anisotropies for the covariances may be introduced in a well-controlled way are examined. These methods permit an analysis scheme to possess covariance structures with adaptive variations of amplitude, scale, profile shape, and degrees of local anisotropy, all as functions of geographical location and altitude. First, it is shown how a wider and more useful variety of covariance shapes than just the Gaussian may be obtained by the positive superposition of Gaussian components of different scales, or by further combinations of these operators with the application of Laplacian operators in order for the products to possess negative sidelobes in their radial profiles. Then it is shown how the techniques of recursive filters may be generalized to admit the construction of covariances whose characteristic scales relative to the grid become adaptive to geographical location, while preserving the necessary properties of self-adjointness and positivity. Special attention is paid to the problems of amplitude control for these spatially inhomogeneous filters and an estimate for the kernel amplitude is proposed based upon an asymptotic analysis of the problem. Finally, a further generalization of the filters that enables fully anisotropic and geographically adaptive covariances to be constructed in a computationally efficient way is discussed.


Related Articles

  • Numerical Aspects of the Application of Recursive Filters to Variational Statistical Analysis. Part I: Spatially Homogeneous and Isotropic Gaussian Covariances. Purser, R. James; Wu, Wan-Shu; Parrish, David F.; Roberts, Nigel M. // Monthly Weather Review;Aug2003 Parts 1 and 2, Vol. 131 Issue 8, p1524 

    The construction and application of efficient numerical recursive filters for the task of convolving a spatial distribution of "forcing" terms with a quasi-Gaussian self-adjoint smoothing kernel in two or three dimensions are described. In the context of variational analysis, this smoothing...

  • On the Smoothing Estimation Problem for the Intensity of a DSMPP. Fernández-Alcalá, Rosa; Navarro-Moreno, Jesus; Ruiz-Molina, Juan // Methodology & Computing in Applied Probability;Mar2012, Vol. 14 Issue 1, p5 

    The smoothing estimation problem for the intensity process of a doubly stochastic multichannel Poisson process is investigated. Recursive procedures for the efficient computation of the fixed-point as well as the fixed-interval smoothing estimators of the intensity process are designed. The only...

  • Application of the credibility theory based on important mathematical properties. Atanasiu, V. // Applied Sciences;2013, Vol. 15, p13 

    In this article we introduce the original BÄuhlmann model, which involves only one isolated contract. We present the best linear credibility estimators for this model and we consider the as application of the optimal credibility estimator of BÄuhlmann, the recursive credibility model...

  • Recent advances to model anisotropic space—time data. Mateu, J.; Porcu, E.; Gregori, P. // Statistical Methods & Applications;2008, Vol. 17 Issue 2, p209 

    Building new and flexible classes of nonseparable spatio-temporal covariances and variograms has resulted a key point of research in the last years. The goal of this paper is to present an up-to-date overview of recent spatio-temporal covariance models taking into account the problem of spatial...

  • Basic concepts of group sequential and adaptive group sequential test procedures. Wassmer, Gernot // Statistical Papers;2000, Vol. 41 Issue 3, p253 

    Examines the basic concepts of repeated significance test procedures. Review of related literature on the repeated significance testing; Notations and the recursive integration formula in the tests; Discussion on adaptive sequential test procedures.

  • Experimental Study of the GPC Applied to Separately Excited DC Motor. Nadir, Bouchetata; Mohamed, Bourahla; Ghalem, Bachir // European Journal of Scientific Research;8/25/2011, Vol. 58 Issue 3, p316 

    The generalized predictive control represents one of the most techniques used in electric motors control. It appears as a solution for control problems of systems with variable dynamics. It's based on the principle of system parameters identification using the inputs and the outputs of the...

  • A moment closure method for stochastic reaction networks. Lee, Chang Hyeong; Kim, Kyeong-Hun; Kim, Pilwon // Journal of Chemical Physics;4/7/2009, Vol. 130 Issue 13, p134107 

    In this paper we present a moment closure method for stochastically modeled chemical or biochemical reaction networks. We derive a system of differential equations which describes the dynamics of means and all central moments from a chemical master equation. Truncating the system for the central...

  • LETTER TO THE EDITOR. ACAN, HUSEYIN; HITCZENKO, PAWEŁ // Journal of Applied Probability;Sep2015, Vol. 52 Issue 3, p904 

    No abstract available.

  • Transverse nearest neighbor degeneracies on a 2×N lattice. Fuller, William Roger // Journal of Mathematical Physics;Aug86, Vol. 27 Issue 8, p2039 

    An exact 15-term recursion relation and the associated generating function are derived for the number of arrangements of q particles on a 2×N lattice such that s occupied nearest neighbor pairs, v of which are transverse, and t unoccupied nearest neighbor pairs are formed.


Read the Article


Sorry, but this item is not currently available from your library.

Try another library?
Sign out of this library

Other Topics