翻訳と辞書 Words near each other ・ Admiralty, Hong Kong ・ Admiralty, Sembawang ・ Admirandopora ・ Admiration ・ Admirał floty ・ Admire Formation ・ Admire Group ・ Admire Moon ・ Admire Rakti ・ Admire, Kansas ・ Admire, Pennsylvania ・ Admirável Chip Novo ・ Admirável Mundo Novo ・ Admissibility ・ Admissible algebra ・ Admissible decision rule ・ Admissible evidence ・ Admissible heuristic ・ Admissible numbering ・ Admissible ordinal ・ Admissible representation ・ Admissible rule ・ Admissible set ・ Admissible trading strategy ・ Admission ・ Admission (film) ・ Admission (law) ・ Admission by Guts ・ Admission control ・ Admission Day Monument 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 Admissible decision rule ： ウィキペディア英語版 Admissible decision rule In statistical decision theory, an admissible decision rule is a rule for making a decision such that there is not any other rule that is always "better" than it.〔Dodge, Y. (2003) ''The Oxford Dictionary of Statistical Terms''. OUP. ISBN 0-19-920613-9 (entry for admissible decision function)〕 Generally speaking, in most decision problems the set of admissible rules is large, even infinite, so this is not a sufficient criterion to pin down a single rule, but as will be seen there are some good reasons to favor admissible rules; compare Pareto efficiency. ==Definition== Define sets $\backslash Theta\backslash ,$, $\backslash mathcal$ and $\backslash mathcal$, where $\backslash Theta\backslash ,$ are the states of nature, $\backslash mathcal$ the possible observations, and $\backslash mathcal$ the actions that may be taken. An observation $x\; \backslash in\; \backslash mathcal\backslash ,\backslash !$ is distributed as $F(x\backslash mid\backslash theta)\backslash ,\backslash !$ and therefore provides evidence about the state of nature $\backslash theta\backslash in\backslash Theta\backslash ,\backslash !$. A decision rule is a function $\backslash delta:\}$, where upon observing $x\backslash in\; \backslash mathcal$, we choose to take action $\backslash delta(x)\backslash in\; \backslash mathcal\backslash ,\backslash !$. Also define a loss function $L:\; \backslash Theta\; \backslash times\; \backslash mathcal\; \backslash rightarrow\; \backslash mathbb$, which specifies the loss we would incur by taking action $a\; \backslash in\; \backslash mathcal$ when the true state of nature is $\backslash theta\; \backslash in\; \backslash Theta$. Usually we will take this action after observing data $x\; \backslash in\; \backslash mathcal$, so that the loss will be $L(\backslash theta,\backslash delta(x))\backslash ,\backslash !$. (It is possible though unconventional to recast the following definitions in terms of a utility function, which is the negative of the loss.) Define the risk function as the expectation :$R(\backslash theta,\backslash delta)=\backslash operatorname\_()\}.\backslash ,\backslash !$ Whether a decision rule $\backslash delta\backslash ,\backslash !$ has low risk depends on the true state of nature $\backslash theta\backslash ,\backslash !$. A decision rule $\backslash delta^$ *\,\! dominates a decision rule $\backslash delta\backslash ,\backslash !$ if and only if $R(\backslash theta,\backslash delta^$ *)\le R(\theta,\delta) for all $\backslash theta\backslash ,\backslash !$, ''and'' the inequality is strict for some $\backslash theta\backslash ,\backslash !$. A decision rule is admissible (with respect to the loss function) if and only if no other rule dominates it; otherwise it is inadmissible. Thus an admissible decision rule is a maximal element with respect to the above partial order. An inadmissible rule is not preferred (except for reasons of simplicity or computational efficiency), since by definition there is some other rule that will achieve equal or lower risk for ''all'' $\backslash theta\backslash ,\backslash !$. But just because a rule $\backslash delta\backslash ,\backslash !$ is admissible does not mean it is a good rule to use. Being admissible means there is no other single rule that is ''always'' better - but other admissible rules might achieve lower risk for most $\backslash theta\backslash ,\backslash !$ that occur in practice. (The Bayes risk discussed below is a way of explicitly considering which $\backslash theta\backslash ,\backslash !$ occur in practice.) 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「Admissible decision rule」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.