Statistical and Numerical Computing
Published Online: 15 SEP 2006
Copyright © 2002 John Wiley & Sons, Ltd
Encyclopedia of Environmetrics
How to Cite
Jorgensen, M. 2006. EM Algorithm. Encyclopedia of Environmetrics. 2.
- Published Online: 15 SEP 2006
The Expectation-maximization (EM) algorithm is an approach to maximum likelihood estimation in complex statistical models that avoids confronting the main optimization problem head-on but rather seeks to piggyback on known solutions to simpler, but related problems. A typical application lies in fitting finite mixtures of probability distributions to a set of observations: this would often be simply done if we knew how to assign each observation to its correct component. The EM algorithm provides a way to use our knowledge of how to solve the simpler problem to help solve the actual problem that we are faced with. The EM algorithm is best understood through examples, and two of these are developed in some detail in this article alongside the necessary theory and references to a range of applications in the literature.