Stochastic EM algorithm for approximating the maximum likelihood estimate

摘要

Stochastic EM is an algorithm designed to handle missing data in statistical applications. Instead of performing the expectation step in the Expectation-Maximization (EM) algorithm, Stochastic EM impute a sample value drawn from the conditional distribution of the missing data given the parameter. This paper explains how the algorithm can be applied in statistical inference to avoid numerical integrations and presents two examples using the Stochastic EM algorithm. The first example deals with censored Weibull data and the second example deals with an empirical Bayes model that arises in educational testing. Some variants of the algorithm are also discussed. This report only treats the theory underlying the Stochastic EM briefly. The properties of the Stochastic EM estimates are dealt with in depth in a sequel of this report.