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EM Algorithm

Statistical and Numerical Computing

  1. Murray Jorgensen

Published Online: 15 SEP 2006

DOI: 10.1002/9780470057339.vae020

Encyclopedia of Environmetrics

Encyclopedia of Environmetrics

How to Cite

Jorgensen, M. 2006. EM Algorithm. Encyclopedia of Environmetrics. 2.

Author Information

  1. University of Waikato, New Zealand

Publication History

  1. 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.