Maximum Likelihood from Incomplete Data Via the EM Algorithm

Abstract

Read before the ROYAL STATISTICAL SOCIETY at a meeting organized by the RESEARCH SECTION on Wednesday, December 8th, 1976, Professor S. D. SILVEY in the Chair] 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.

Learning chaotic dynamics under noise with on-line EM algorithm

“…, T}, the model parameter T of the stochastic model (2) can be determined by the maximum likelihood estimation method. In particular, the EM algorithm [1] can be applied to a stochastic model with hidden variables. The EM algorithm repeats the following E-and M-steps.…”

Rater agreement and the generalized Rudas-Clogg-Lindsay index of fit

“…Although the mixture models which include an unstructured component are overparametrized, no substantial estimation problems were observed because maximum likelihood parameter estimation was realized by a program [2] which uses the EM algorithm [6]. To ensure safe performance of the EM algorithm, the starting values should be chosen to be the parameter estimates of the corresponding log-linear model or mixture model excluding the unstructured component.…”

Mapping a quantitative trait locus via the EM algorithm and Bayesian classification

“…A computationally simpler and more elegant procedure is based on the EM algorithm corresponding to a mixture of normal populations [Dempster et al, 1977;McLachlan and Krishnan, 1997]. A sketch of the algorithm is presented below.…”