Dynamics of the Fisher information metric

Abstract

Article (Published Version) http://sro.sussex.ac.uk Calmet, Xavier and Calmet, Jaques (2005) Dynamics of the Fisher information metric. Physical Review E, 71 (5). ISSN 1539-3755 This version is available from Sussex Research Online: http://sro.sussex.ac.uk/15301/ This document is made available in accordance with publisher policies and may differ from the published version or from the version of record. If you wish to cite this item you are advised to consult the publisher's version. Please see the URL above for details on accessing the published version. Copyright and reuse:Sussex Research Online is a digital repository of the research output of the University.Copyright and all moral rights to the version of the paper presented here belong to the individual author(s) and/or other copyright owners. To the extent reasonable and practicable, the material made available in SRO has been checked for eligibility before being made available.Copies of full text items generally can be reproduced, displayed or performed and given to third parties in any format or medium for personal research or study, educational, or not-for-profit purposes without prior permission or charge, provided that the authors, title and full bibliographic details are credited, a hyperlink and/or URL is given for the original metadata page and the content is not changed in any way. We present a method to generate probability distributions that correspond to metrics obeying partial differential equations generated by extremizing a functional J͓g ͑ i ͔͒, where g ͑ i ͒ is the Fisher metric. We postulate that this functional of the dynamical variable g ͑ i ͒ is stationary with respect to small variations of these variables. Our approach enables a dynamical approach to the Fisher information metric. It allows one to impose symmetries on a statistical system in a systematic way. Dynamics of the Fisher information metric

Fisher information metric for the Langevin equation and least informative models of continuous stochastic dynamics

“…If a ξ ∈ [0, 1] variable is employed to specify the state of model parameters and interpolate between two different sets of parameters, the Fisher information metric can be used to quantify the information change in varying the parameter set 23,43…”

On important information for inverse problems and its visualization

“…Следует также отметить, что сообщества исследователей, использующих сопряженные уравнения [10,16,17], информационную динамику [13], статистическое решение обратных задач [4,6,11], скалярные инварианты тензорной информации [3,18] в основном не осознают наличия некоторой общей информационной основы.…”

“…Тензорная компонента ценной информации (информационная матрица Фишера) является наиболее сложным элементом с точки зрения вычислений. Формально она может быть рассчитана с помощью уравнений информационной динамики типа Эйнштейна [13]…”

Distance Between Physical Theories Based on Information Theory

“…Furthermore, it has been shown that Fisher's metric can be derived from an action. 8 It would be interesting to see if imposing symmetries at the level of the action can lead to interesting relations between physical models.…”