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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 estimator ： ウィキペディア英語版 Bayes estimator In estimation theory and decision theory, a Bayes estimator or a Bayes action is an estimator or decision rule that minimizes the posterior expected value of a loss function (i.e., the posterior expected loss). Equivalently, it maximizes the posterior expectation of a utility function. An alternative way of formulating an estimator within Bayesian statistics is maximum a posteriori estimation. ==Definition== Suppose an unknown parameter θ is known to have a prior distribution $\backslash pi$. Let $\backslash widehat\; =\; \backslash widehat(x)$ be an estimator of θ (based on some measurements ''x''), and let $L(\backslash theta,\backslash widehat)$ be a loss function, such as squared error. The Bayes risk of $\backslash widehat$ is defined as $E\_\backslash pi(L(\backslash theta,\; \backslash widehat))$, where the expectation is taken over the probability distribution of $\backslash theta$: this defines the risk function as a function of $\backslash widehat$. An estimator $\backslash widehat$ is said to be a ''Bayes estimator'' if it minimizes the Bayes risk among all estimators. Equivalently, the estimator which minimizes the posterior expected loss $E(L(\backslash theta,\backslash widehat)\; |\; x)$ ''for each x'' also minimizes the Bayes risk and therefore is a Bayes estimator.〔Lehmann and Casella, Theorem 4.1.1〕 If the prior is improper then an estimator which minimizes the posterior expected loss ''for each x'' is called a generalized Bayes estimator.〔Lehmann and Casella, Definition 4.2.9〕 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「Bayes estimator」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.