Topic
Expectation–maximization algorithm
About: Expectation–maximization algorithm is a research topic. Over the lifetime, 11823 publications have been published within this topic receiving 528693 citations. The topic is also known as: EM algorithm & Expectation Maximization.
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TL;DR: It is proved that the reliability of an arbitrary system can be approximated well by a finite Weibull mixture with positive component weights only, without knowing the structure of the system, on condition that the unknown parameters of the mixture can be estimated.
92 citations
TL;DR: In this article, a single-step maximum likelihood estimation procedure for multidimensional scaling of dissimilarity data measured on rating scales is developed for multi-dimensional scaling data, which can fit the euclidian distance model to the data under various assumptions about category widths.
Abstract: A single-step maximum likelihood estimation procedure is developed for multidimensional scaling of dissimilarity data measured on rating scales. The procedure can fit the euclidian distance model to the data under various assumptions about category widths and under two distributional assumptions. The scoring algorithm for parameter estimation has been developed and implemented in the form of a computer program. Practical uses of the method are demonstrated with an emphasis on various advantages of the method as a statistical procedure.
92 citations
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TL;DR: In this paper, the score vector for a time series model which fits into the Gaussian state space form can be approximated by numerically differentiating the log-likelihood.
Abstract: The score vector for a time series model which fits into the Gaussian state space form can be approximated by numerically differentiating the log-likelihood. If the parameter vector is of length p, this involves the running of p + 1 Kalman filters. This paper shows the score vector can be computed in a single pass of the Kalman filter and a smoother. For many classes of models this dramatically increases the speed and reliability of algorithms for the numerical maximisation of likelihood.
92 citations
TL;DR: In this article, the authors show that iterative methods for maximizing the likelihood in a mixture of exponentials model depend strongly on their particular implementation Different starting strategies and stopping rules yield completely different estimators of the parameters.
Abstract: We show that iterative methods for maximizing the likelihood in a mixture of exponentials model depend strongly on their particular implementation Different starting strategies and stopping rules yield completely different estimators of the parameters This is demonstrated for the likelihood ratio test of homogeneity against two-component exponential mixtures, when the test statistic is calculated by the EM algorithm
92 citations
TL;DR: An algorithm similar to the well-known Baum-Welch (1970) algorithm for estimating the parameters of a hidden Markov model (HMM) is derived that is equivalent to maximizing the likelihood function for the standard parameterization of the HMM defined on the input data space.
Abstract: We derive an algorithm similar to the well-known Baum-Welch (1970) algorithm for estimating the parameters of a hidden Markov model (HMM). The new algorithm allows the observation PDF of each state to be defined and estimated using a different feature set. We show that estimating parameters in this manner is equivalent to maximizing the likelihood function for the standard parameterization of the HMM defined on the input data space. The processor becomes optimal if the state-dependent feature sets are sufficient statistics to distinguish each state individually from a common state.
92 citations