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In Bayesian statistics, a maximum a posteriori probability (MAP) estimate is a mode of the posterior distribution. The MAP can be used to obtain a point estimate of an unobserved quantity on the basis of empirical data. It is closely related to Fisher's method of maximum likelihood (ML), but employs an augmented optimization objective which incorporates a prior distribution over the quantity one wants to estimate. MAP estimation can therefore be seen as a regularization of ML estimation. ==Description== Assume that we want to estimate an unobserved population parameter on the basis of observations . Let be the sampling distribution of , so that is the probability of when the underlying population parameter is . Then the function: : is known as the likelihood function and the estimate: : where is density function of , is the domain of . This is a straightforward application of Bayes' theorem. The method of maximum a posteriori estimation then estimates as the mode of the posterior distribution of this random variable: : as goes to 0, the sequence of Bayes estimators approaches the MAP estimator, provided that the distribution of is unimodal. But generally a MAP estimator is not a Bayes estimator unless is discrete. 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「maximum a posteriori estimation」の詳細全文を読む スポンサード リンク
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