The EM algorithm : an overview with applications to medical data

• Main Author: Coupal, Louis
• Format: Others
• Language: en
• Published: McGill University 1992
• Subjects: Statistics.
• Online Access: http://digitool.Library.McGill.CA:80/R/?func=dbin-jump-full&object_id=56644

Owing to their complex design and use of live subjects as experimental units, missing or incomplete data is common place in medical experiments. The great increase in difficulty of maximum likelihood based analysis of incomplete data experiments compared to a similar complete data analysis encourages many medical researchers to ignore cases with missing data in favour of performing a "complete" cases analysis. === The expectation maximization algorithm (EM for short) is often an easily implemented algorithm that provides estimates of parameters in models with missing data. The EM algorithm unifies the theory of maximum likelihood estimation in the context of "missing" data. The general problem of missing data also includes structurally unobservable quantities such as parameters, hyperparameters and latent variables. The nature of its defining steps, the expectation or E-step and the maximization or M-step, gives the user intuitive understanding of the maximization process. === In this Thesis, the EM algorithm is first illustrated through an example borrowed from the field of genetics. The theory of the EM algorithm is formally developed and the special case of exponential families is considered. Issues concerning convergence and inference are discussed. Many examples taken from the medical literature serve to highlight the method's broad spectrum of application in both missing data and unobservable parameter problems.