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In statistics, maximum-likelihood estimation (MLE) is a method of estimating the parameters of a statistical model given data. The method of maximum likelihood corresponds to many well-known estimation methods in statistics. For example, one may be interested in the heights of adult female penguins, but be unable to measure the height of every single penguin in a population due to cost or time constraints. Assuming that the heights are normally distributed with some unknown mean and variance, the mean and variance can be estimated with MLE while only knowing the heights of some sample of the overall population. MLE would accomplish this by taking the mean and variance as parameters and finding particular parametric values that make the observed results the most probable given the model. In general, for a fixed set of data and underlying statistical model, the method of maximum likelihood selects the set of values of the model parameters that maximizes the likelihood function. Intuitively, this maximizes the "agreement" of the selected model with the observed data, and for discrete random variables it indeed maximizes the probability of the observed data under the resulting distribution. Maximum-likelihood estimation gives a unified approach to estimation, which is well-defined in the case of the normal distribution and many other problems. However, in some complicated problems, difficulties do occur: in such problems, maximum-likelihood estimators are unsuitable or do not exist. == History == Maximum-likelihood estimation was recommended, analyzed (with fruitless attempts at proofs) and vastly popularized by Ronald Fisher between 1912 and 1922〔Parametric statistical theory Pfanzagl, Johann, with the assistance of R. Hamböker 1994 publisher, Walter de Gruyter, Berlin, DE isbn=3-11-013863-8 pages=207–208〕 (although it had been used earlier by Carl Friedrich Gauss, Pierre-Simon Laplace, Thorvald N. Thiele, and Francis Ysidro Edgeworth).〔 and 〕 Reviews of the development of maximum likelihood have been provided by a number of authors.〔, , , , and 〕 Some of the theory behind maximum-likelihood estimation was developed for Bayesian statistics.〔 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 likelihood」の詳細全文を読む スポンサード リンク
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