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翻訳と辞書　辞書検索 [ 開発暫定版 ] スポンサード リンク Observed information ： ウィキペディア英語版 Observed information In statistics, the observed information, or observed Fisher information, is the negative of the second derivative (the Hessian matrix) of the "log-likelihood" (the logarithm of the likelihood function). It is a sample-based version of the Fisher information. ==Definition== Suppose we observe random variables $X\_1,\backslash ldots,X\_n$, independent and identically distributed with density ''f''(''X''; θ), where θ is a (possibly unknown) vector. Then the log-likelihood of the parameters $\backslash theta$ given the data $X\_1,\backslash ldots,X\_n$ is :$\backslash ell(\backslash theta\; |\; X\_1,\backslash ldots,X\_n)\; =\; \backslash sum\_^n\; \backslash log\; f(X\_i|\; \backslash theta)$. We define the observed information matrix at $\backslash theta^$ as :$\backslash mathcal(\backslash theta^$ *) = - \left. \nabla \nabla^ \ell(\theta) \right|_ ::$=\; -$ \left. \left( \begin \tfrac & \tfrac & \cdots & \tfrac \\ \tfrac & \tfrac & \cdots & \tfrac \\ \vdots & \vdots & \ddots & \vdots \\ \tfrac & \tfrac & \cdots & \tfrac \\ \end \right) \ell(\theta) \right|_ In many instances, the observed information is evaluated at the maximum-likelihood estimate.〔Dodge, Y. (2003) ''The Oxford Dictionary of Statistical Terms'', OUP. ISBN 0-19-920613-9〕 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「Observed information」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.