Mixture Densities, Maximum Likelihood and the EM Algorithm
Abstract
The problem of estimating the parameters which determine a mixture density has been the subject of a large, diverse body of literature spanning nearly ninety years. During the last two decades, the method of maximum likelihood has become the most widely followed approach to this problem, thanks primarily to the advent of high speed electronic computers. Here, we first offer a brief survey of the literature directed toward this problem and review maximum-likelihood estimation for it. We then turn to the subject of ultimate interest, which is a particular iterative procedure for numerically approximating maximum-likelihood estimates for mixture density problems. This procedure, known as the EM algorithm, is a specialization to the mixture density context of a general algorithm of the same name used to approximate maximum-likelihood estimates for incomplete data problems. We discuss the formulation and theoretical and practical properties of the EM algorithm for mixture densities, focussing in particular on mixtures of densities from exponential families.
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Copyright © 1984 Society for Industrial and Applied Mathematics.
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Submitted: 6 April 1982
Accepted: 5 August 1983
Published online: 10 July 2006
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- A review of semiparametric mixture modelsJournal of Statistical Planning and Inference, Vol. 47, No. 1-2 | 1 Oct 1995