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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 Bayes' rule ： ウィキペディア英語版 Bayes' rule In probability theory and applications, Bayes's rule relates the odds of event $A\_1$ to the odds of event $A\_2$, before (prior to) and after (posterior to) conditioning on another event $B$. The odds on $A\_1$ to event $A\_2$ is simply the ratio of the probabilities of the two events. The prior odds is the ratio of the unconditional or prior probabilities, the posterior odds is the ratio of conditional or posterior probabilities given the event $B$. The relationship is expressed in terms of the likelihood ratio or Bayes factor, $\backslash Lambda$. By definition, this is the ratio of the conditional probabilities of the event $B$ given that $A\_1$ is the case or that $A\_2$ is the case, respectively. The rule simply states: posterior odds equals prior odds times Bayes factor (Gelman et al., 2005, Chapter 1). When arbitrarily many events $A$ are of interest, not just two, the rule can be rephrased as posterior is proportional to prior times likelihood, $P(A|B)\backslash propto\; P(A)\; P(B|A)$ where the proportionality symbol means that the left hand side is proportional to (i.e., equals a constant times) the right hand side as $A$ varies, for fixed or given $B$ (Lee, 2012; Bertsch McGrayne, 2012). In this form it goes back to Laplace (1774) and to Cournot (1843); see Fienberg (2005). Bayes' rule is an equivalent way to formulate Bayes' theorem. If we know the odds for and against $A$ we also know the probabilities of $A$. It may be preferred to Bayes' theorem in practice for a number of reasons. Bayes' rule is widely used in statistics, science and engineering, for instance in model selection, probabilistic expert systems based on Bayes networks, statistical proof in legal proceedings, email spam filters, and so on (Rosenthal, 2005; Bertsch McGrayne, 2012). As an elementary fact from the calculus of probability, Bayes' rule tells us how unconditional and conditional probabilities are related whether we work with a frequentist interpretation of probability or a Bayesian interpretation of probability. Under the Bayesian interpretation it is frequently applied in the situation where $A\_1$ and $A\_2$ are competing hypotheses, and $B$ is some observed evidence. The rule shows how one's judgement on whether $A\_1$ or $A\_2$ is true should be updated on observing the evidence $B$ (Gelman et al., 2003). ==The rule== 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「Bayes' 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.