**
StATS: EM Algorithm (March 15, 2004)**.

I received an email question about the EM Algorithm. This is a computational approach that works well for missing data problems and data models with latent (unobserved) variabels. The basic approach is to estimate the missing or latent data (E-step), compute maximum likelihood estimates that incorporates the missing/latent estimates (M-step), then update the missing or latent data (E-step) and so forth. There's a book by McLachlan and Krishnan, The EM Algorithm and Extensions, that I have not seen, but which sounds pretty good. There are also a few good web sites about this algorithm.

**The Expectation
Maximization Algorithm [pdf]**. Dellaert F, Georgia Institute of Technology.
Accessed on 2004-03-15. www.cc.gatech.edu/~dellaert/em-paper.pdf

**The EM
Algorithm and its Extensions**. Bell Laboratories. Accessed on 2004-03-15.
cm.bell-labs.com/cm/ms/departments/sia/project/em/

**A Gentle Tutorial of
the EM Algorithm and its Application to Parameter Estimation for Gaussian Mixture and Hidden
Markov Models [pdf]**. Bilmes JA, U.C. Berkeley. Accessed on 2004-03-15.
www.vision.ethz.ch/ml/slides/em_tutorial.pdf

If I get some time, I will show a simple example on my web pages.

This page was written by Steve Simon while working at Children's Mercy Hospital. Although I do not hold the copyright for this material, I am reproducing it here as a service, as it is no longer available on the Children's Mercy Hospital website. Need more information? I have a page with general help resources. You can also browse for pages similar to this one at Category: Statistical computing.