EM算法理论及其应用

EM Algorithm and Its Applications

EM算法是一种迭代算法,主要用来计算后验分布的众数或极大似然估计,广泛地应用于缺损数据、截尾数据、成群数据、带有讨厌参数的数据等所谓的不完全数据的统计推断问题。在介绍EM算法的基础上,针对EM算法收敛速度慢的缺陷,具体讨论了加速EM算法:EMB算法和MEMB算法;针对EM算法计算的局限性,给出了EM算法的推广:GEM和MCEM算法。最后给出了EM的实值实例,结果精确。

EM algorithm, a method of iteration, is mainly used to calculate the mode of a posterior distribution or the maximum likelihood estimate. EM algorithm has been widely applied to statistical inferences involving incomplete data such as missing data, censoring data, group data and data bearing disgusting parameters. This thesis firstly introduces EM algorithm. To deal with the defects of EM algorithm＇s slow convergence speed, the accelerating EM algorithms, namely EMB algorithm and MEMB algorithm are introduced. We also briefly introduce the two generalized methods, GEM algorithm and MCEM algorithm, to avoid its limitations. The thesis gives the examples and Monte Carlo simulations in the end. By designing MATLAB programs we obtain and analyze the results.