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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 Expected value of sample information ： ウィキペディア英語版 Expected value of sample information In decision theory, the expected value of sample information (EVSI) is the expected increase in utility that you could obtain from gaining access to a sample of additional observations before making a decision. The additional information obtained from the sample may allow you to make a more informed, and thus better, decision, thus resulting in an increase in expected utility. EVSI attempts to estimate what this improvement would be before seeing actual sample data; hence, EVSI is a form of what is known as ''preposterior analysis''. == Formulation == Let :$$ \begin d\in D & \mbox D \\ x\in X & \mbox X \\ z \in Z & \mbox n \mbox \langle z_1,z_2,..,z_n \rangle \\ U(d,x) & \mbox d \mbox x \\ p(x) & \mbox x \\ p(z|x) & \mbox z \end It is common (but not essential) in EVSI scenarios for $Z\_i=X$, $p(z|x)=\backslash prod\; p(z\_i|x)$ and $\backslash int\; z\; p(z|x)\; dz\; =\; x$, which is to say that each observation is an unbiased sensor reading of the underlying state $x$, with each sensor reading being independent and identically distributed. The utility from the optimal decision based only on your prior, without making any further observations, is given by :$$ E() = \max_ ~ \int_X U(d,x) p(x) ~ dx If you could gain access to a single sample, $z$, the optimal posterior utility would be: :$$ E() = \max_ ~ \int_X U(d,x) p(x|z) ~ dx where $p(x|z)$ is obtained from Bayes' rule: :$$ p(x|z) = :$$ p(z) = \int p(z|x) p(x) ~ dx Since you don't know what sample would actually be obtained if you were to obtain a sample, you must average over all possible samples to obtain the expected utility given a sample: :$$ E() = \int_Z E() p(z) dz = \int_Z \max_ ~ \int_X U(d,x) p(z|x) p(x) ~ dx ~ dz The expected value of sample information is then defined as: :$$ \begin EVSI & = E() - E() \\ & = \left(\int_Z \max_ ~ \int_X U(d,x) p(z|x) p(x) ~ dx ~ dz\right) - \left(\max_ ~ \int_X U(d,x) p(x) ~ dx\right) \end 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「Expected value of sample 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.