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.

Keywords

  1. mixture densities
  2. maximum likelihood
  3. EM algorithm
  4. exponential families
  5. incomplete data

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cover image SIAM Review
SIAM Review
Pages: 195 - 239
ISSN (online): 1095-7200

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Submitted: 6 April 1982
Accepted: 5 August 1983
Published online: 10 July 2006

Keywords

  1. mixture densities
  2. maximum likelihood
  3. EM algorithm
  4. exponential families
  5. incomplete data

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