Fisher information under Gaussian quadrature models

Fisher Information in Gaussian Graphical Models

This note summarizes various derivations, formulas and computational algorithms relevant to the Fisher information matrix of Gaussian graphical models with respect to either an exponential parameterization (related to the information form) or the corresponding moment parameterization. 1 Gauss-Markov Models The probability density of a Gaussian random vector x ∈ R may be expressed in information...

Fisher information under decoherence in Bloch representation

Wei Zhong,1,2 Zhe Sun,1,3 Jian Ma,1,2 Xiaoguang Wang,1,2,* and Franco Nori1,4 1Advanced Science Institute, RIKEN, Wako-shi, Saitama 351-0198, Japan 2Zhejiang Institute of Modern Physics, Department of Physics, Zhejiang University, Hangzhou 310027, China 3Department of Physics, Hangzhou Normal University, Hangzhou 310036, China 4Physics Department, The University of Michigan, Ann Arbor, Michigan...

Information entropy of Gegenbauer polynomials and Gaussian quadrature

In a recent paper (Buyarov V S, López-Artés P, Martı́nez-Finkelshtein A and Van Assche W 2000 J. Phys. A: Math. Gen. 33 6549–60), an efficient method was provided for evaluating in closed form the information entropy of the Gegenbauer polynomials C n (x) in the case when λ = l ∈ N. For given values of n and l, this method requires the computation by means of recurrence relations of two auxiliary...

Anti-Gaussian quadrature formulas

An anti-Gaussian quadrature formula is an (n+ 1)-point formula of degree 2n− 1 which integrates polynomials of degree up to 2n+ 1 with an error equal in magnitude but of opposite sign to that of the n-point Gaussian formula. Its intended application is to estimate the error incurred in Gaussian integration by halving the difference between the results obtained from the two formulas. We show tha...

The Gaussian Quadrature Method