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第29行： + + − 算法在1977年由 Arthur Dempster，Nan Laird 和 Donald Rubin 发表的一篇经典论文中得到了解释和命名。他们指出，这种方法是早期作者”在特殊情况下多次提出的”。其中最早的是塞德里克 · 史密斯估计等位基因频率的基因计数法。罗尔夫 · 桑德伯格在他的论文和几篇论文中对指数族的 EM 方法进行了非常详细的论述，这些论文是在他与 Per Martin-Löf 和 Anders Martin-Löf 合作之后发表的。<！-- * Martin-Löf，p. “精确测试，置信区域和估计” ，由 a. w. f. Edwards，g. a. Barnard，d. a. Sprott，o. Barndorff-Nielsen，d. Basu 和 g. Rasch 讨论。推论统计学基本问题会议论文集(奥尔胡斯，1973) ，页。121–138.回忆录，没有。1，Dept. .照相机。印第安州 statist. 。Math. 大学。Aarhus, Aarhus, 1974.Dempster-Laird-Rubin 于1977年发表的论文对该方法进行了推广，并对一类更广泛的问题进行了收敛性分析。Dempster-Laird-Rubin 论文建立了 EM 方法作为统计分析的重要工具。
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The EM algorithm was explained and given its name in a classic 1977 paper by Arthur Dempster, Nan Laird, and Donald Rubin. They pointed out that the method had been "proposed many times in special circumstances" by earlier authors. One of the earliest is the gene-counting method for estimating allele frequencies by Cedric Smith. A very detailed treatment of the EM method for exponential families was published by Rolf Sundberg in his thesis and several papers following his collaboration with Per Martin-Löf and Anders Martin-Löf.<!-- * Martin-Löf, P. "Exact tests, confidence regions and estimates", with a discussion by A. W. F. Edwards, G. A. Barnard, D. A. Sprott, O. Barndorff-Nielsen, D. Basu and G. Rasch. Proceedings of Conference on Foundational Questions in Statistical Inference (Aarhus, 1973), pp. 121–138. Memoirs, No. 1, Dept. Theoret. Statist., Inst. Math., Univ. Aarhus, Aarhus, 1974. --> The Dempster–Laird–Rubin paper in 1977 generalized the method and sketched a convergence analysis for a wider class of problems. The Dempster–Laird–Rubin paper established the EM method as an important tool of statistical analysis.
The EM algorithm was explained and given its name in a classic 1977 paper by Arthur Dempster, Nan Laird, and Donald Rubin. They pointed out that the method had been "proposed many times in special circumstances" by earlier authors. One of the earliest is the gene-counting method for estimating allele frequencies by Cedric Smith. A very detailed treatment of the EM method for exponential families was published by Rolf Sundberg in his thesis and several papers following his collaboration with Per Martin-Löf and Anders Martin-Löf.<!-- * Martin-Löf, P. "Exact tests, confidence regions and estimates", with a discussion by A. W. F. Edwards, G. A. Barnard, D. A. Sprott, O. Barndorff-Nielsen, D. Basu and G. Rasch. Proceedings of Conference on Foundational Questions in Statistical Inference (Aarhus, 1973), pp. 121–138. Memoirs, No. 1, Dept. Theoret. Statist., Inst. Math., Univ. Aarhus, Aarhus, 1974. --> The Dempster–Laird–Rubin paper in 1977 generalized the method and sketched a convergence analysis for a wider class of problems. The Dempster–Laird–Rubin paper established the EM method as an important tool of statistical analysis.
Arthur Dempster, Nan Laird, and Donald Rubin于1977年发表的一篇经典的论文中解释和命名了EM算法。他们指出该方法被早期作者“多次在特殊条件下提出”。Cedric Smith提出的估计等位基因频率的基因计数法便是其中之一。基于与Per Martin-Löf和Anders Martin-Löf的合作，Rolf Sundberg在他的学位论文和若干论文中详述了针对指数族的EM方法。1977年Dempster–Laird–Rubin的论文推广了该方法并针对更为广泛的问题进行了收敛性分析。
Dempster–Laird–Rubin算法的收敛分析存在缺陷，C. F. Jeff Wu在1983年发表了一项修正的收敛性分析。Wu的工作建立了EM方法在指数族之外的收敛。
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