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1977•Journal of the Royal Statistical Society Series B (Statistical Methodology)Requires access

Maximum Likelihood from Incomplete Data Via the EM Algorithm

A. P. Dempster, N. M. Laird, Donald B. Rubin

Open publisher page 49,842 citations

Abstract

Summary A broadly applicable algorithm for computing maximum likelihood estimates from incomplete data is presented at various levels of generality. Theory showing the monotone behaviour of the likelihood and convergence of the algorithm is derived. Many examples are sketched, including missing value situations, applications to grouped, censored or truncated data, finite mixture models, variance component estimation, hyperparameter estimation, iteratively reweighted least squares and factor analysis.

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What this paper is about

Summary A broadly applicable algorithm for computing maximum likelihood estimates from incomplete data is presented at various levels of generality. Theory showing the monotone behaviour of the likelihood and convergence of the algorithm is derived. Many examples are sketched, including missing value situations, applications to grouped, censored or truncated data, finite mixture models, variance component estimation, hyperparameter estimation, iteratively reweighted least squares and factor analysis.

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OpenAlex reports 49842 citations for this work. Citation counts describe recorded attention and do not establish research quality.

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Available abstract

Summary A broadly applicable algorithm for computing maximum likelihood estimates from incomplete data is presented at various levels of generality. Theory showing the monotone behaviour of the likelihood and convergence of the algorithm is derived. Many examples are sketched, including missing value situations, applications to grouped, censored or truncated data, finite mixture models, variance component estimation, hyperparameter estimation, iteratively reweighted least squares and factor analysis.

Key concepts: Maximum likelihood, Expectation–maximization algorithm, Computer science, Algorithm, Mathematics, Statistics

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