The EM algorithm and medical studies: a historical linik
The EM algorithm and medical studies: a historical linik
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DOI：
10.1177/096228029700600102
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发表时间：
1997-02
影响因子：
2.3
通讯作者：
Xiaonan Meng
中科院分区：
文献类型：
--
作者：
Xiaonan Meng
安德森·格雷·麦肯德里克1926年的论文《数学在医学问题中的应用》是邓普斯特等人最早引用的参考文献。S 1977年发表的论文定义并推广了EM算法。约瑟夫·奥斯卡·欧文在1962年作为英国皇家统计学会主席发表的题为《数学在医学和生物统计学中的地位》的就职演说中，突出地提到了麦肯德里克的论文。麦肯德里克的工作与EM算法的联系是由于欧文对一种新的方法进行了改进，麦肯德里克用来估计感染率的新方法是，当观察数据没有区分那些不容易感染的人和那些容易感染但不会出现症状的人时。本文研究了这一环节，同时说明了EM算法的核心思想及其特性；该研究还提出了一种加速EM的剖析策略，可能值得广泛研究。麦肯德里克关于霍乱流行的数据被用来说明，并将EM与欧文的方法以及牛顿-拉夫森算法进行比较。计算以外的问题也会在适当的时候讨论。
Anderson Gray McKendrick's 1926 paper, `Applications of mathematics to medical problems', was the earliest reference cited in Dempster et al.'s 1977 paper that defined and popularized the EM algorithm. McKendrick's paper was prominently featured by Joseph Oscar Irwin in his 1962 inaugural address as the President of the Royal Statistical Society (in the UK), entitled `The place of mathematics in medical and biological statistics'. The link of McKendrick's work to the EM algorithm is due to an improvement made by Irwin on a novel method McKendrick used for estimating an infection rate when the observed data do not distinguish between those individuals who are not susceptible to the infection and those who are susceptible, but do not develop symptoms. This article examines this link, along the way illustrating the central ideas underlying the EM algorithm as well as its properties; the examination also suggests a profiling strategy for speeding up EM, which may be worthy of general investigation. McKendrick's data on an epidemic of cholera are used for illustration and to compare EM with Irwin's method as well as the Newton-Raphson algorithm. Issues beyond computation are also discussed whenever appropriate.