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Some recent research in the analysis of mixture distributions. (English) Zbl 0714.62023
Summary: The paper describes some recent and particularly innovative topics within the subject of mixture distributions. After a very brief review of the practical importance of the subject, in which the interpretation of mixture data as incomplete data is emphasized, three dependence structures for mixture data are described: the hidden multinomial (corresponding to “traditional” mixture data), the hidden Markov chain and the hidden Markov random field.
Maximum likelihood estimation of parameters is discussed and it is seen that the degree of difficulty increases dramatically as one passes through the three types of dependence structure. Other areas considered are maximum likelihood estimation of a general mixing distribution, identification of the number of components present in a mixture, and the classification problem of identifying the population memberships of all observations in a sample of mixture data. The points of contact with current work in image restoration and segmentation are emphasized.

MSC:
62F10 Point estimation
62M05 Markov processes: estimation; hidden Markov models
62M40 Random fields; image analysis
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