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Model Selection for Mixture Models-Perspectives and Strategies

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CFSR.pdf (868.6Kb)
Date
2018
Indexation documentaire
Analyse
Subject
Mixture Models; Bayesian
Titre de l'ouvrage
Handbook of Mixture Analysis
Auteur
Celeux, Gilles; Frühwirth-Schnatter, Sylvia; Robert, Christian P.
Nom de l'éditeur
CRC Press, Taylor&Francis
Année
2018
Nombre total de pages
498
ISBN
9781498763813
URI
https://basepub.dauphine.fr/handle/123456789/18580
Collections
  • CEREMADE : Publications
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Auteur
Celeux, Gilles
34587 INRIA Rocquencourt
Frühwirth-Schnatter, Sylvia
Robert, Christian P.
60 CEntre de REcherches en MAthématiques de la DEcision [CEREMADE]
2579 Centre de Recherche en Économie et Statistique [CREST]
Type
Chapitre d'ouvrage
Nombre de pages du document
40
Résumé en anglais
Determining the number G of components in a finite mixture distribution is an important and difficult inference issue. This is a most important question, because statistical inference about the resulting model is highly sensitive to the value of G. Selecting an erroneous value of G may produce a poor density estimate. This is also a most difficult question from a theoretical perspective as it relates to unidentifiability issues of the mixture model. This is further a most relevant question from a practical viewpoint since the meaning of the number of components G is strongly related to the modelling purpose of a mixture distribution. We distinguish in this chapter between selecting G as a density estimation problem in Section 2 and selecting G in a model-based clustering framework in Section 3. Both sections discuss frequentist as well as Bayesian approaches. We present here some of the Bayesian solutions to the different interpretations of picking the "right" number of components in a mixture, before concluding on the ill-posed nature of the question.

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