翻訳と辞書 Words near each other ・ Statistical fluctuations ・ Statistical genetics ・ Statistical geography ・ Statistical graphics ・ Statistical hypothesis testing ・ Statistical inference ・ Statistical Institute of Catalonia ・ Statistical interference ・ Statistical Lab ・ Statistical language acquisition ・ Statistical learning in language acquisition ・ Statistical learning theory ・ Statistical Lempel–Ziv ・ Statistical literacy ・ Statistical machine translation ・ Statistical manifold ・ Statistical map ・ Statistical mechanics ・ Statistical Methods for Research Workers ・ Statistical Methods in Medical Research ・ Statistical model ・ Statistical murder ・ Statistical noise ・ Statistical Office of Slovenia ・ Statistical parameter ・ Statistical parametric mapping ・ Statistical parsing ・ Statistical physics ・ Statistical population ・ Statistical potential Dictionary Lists mini英和辞書 mini和英辞書 Webster 1913 Latin-English FOLDOC Wikipedia English ウィキペディア

翻訳と辞書　辞書検索 [ 開発暫定版 ] スポンサード リンク Statistical manifold ： ウィキペディア英語版 Statistical manifold In mathematics, a statistical manifold is a Riemannian manifold, each of whose points is a probability distribution. Statistical manifolds provide a setting for the field of information geometry. The Fisher information metric provides a metric on these manifolds. ==Examples== The family of all normal distributions, parametrized by the expected value ''μ'' and the variance ''σ''2 ≥ 0, with the Riemannian metric given by the Fisher information matrix, is a statistical manifold. Its geometry is modeled on hyperbolic space. A simple example of a statistical manifold, taken from physics, would be the canonical ensemble: it is a one-dimensional manifold, with the temperature ''T'' serving as the coordinate on the manifold. For any fixed temperature ''T'', one has a probability space: so, for a gas of atoms, it would be the probability distribution of the velocities of the atoms. As one varies the temperature ''T'', the probability distribution varies. Another simple example, taken from medicine, would be the probability distribution of patient outcomes, in response to the quantity of medicine administered. That is, for a fixed dose, some patients improve, and some do not: this is the base probability space. If the dosage is varied, then the probability of outcomes changes. Thus, the dosage is the coordinate on the manifold. To be a smooth manifold, one would have to measure outcomes in response to arbitrarily small changes in dosage; this is not a practically realizable example, unless one has a pre-existing mathematical model of dose-response where the dose can be arbitrarily varied. 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Statistical manifold」の詳細全文を読む スポンサード リンク 翻訳と辞書 : 翻訳のためのインターネットリソース Copyright(C) kotoba.ne.jp 1997-2016. All Rights Reserved.