Celeux, Gilles

Numérisation de Documents Anciens Mathématiques

Journal de la Société Française de StatistiqueVol. 160 No. 1 (2019)Editorial of the Special Issue on Mixture AnalysisTitre: Éditorial du numéro spécial sur l’analyse de mélangesGilles Celeux1Since many years, mixture models have taken a great importance in modern statistical inference.Mixture models are hidden structure models allowing to analyse heterogeneity of data oftenoccurring in a lot of domains. Thus mixture models can be viewed as a semi-parametric tool toestimate probability distributions and are also the reference tool in model-based clustering. Theyapply in many contexts such as clustering of independent data, hidden Markov models, clusteringof networks, mixtures of experts models, co-clustering... They involve important, difficult andinteresting questions to be addressed. Choosing a relevant number of mixture components is notthe least one.As a mater of fact, mixture models lead to authoritative monographs along the years. Thebook of [Titterington et al., 1985] can be recommended in particular for its presentation of thebasic mathematical characteristics of mixture models. The book of [McLachlan and Peel, 2000]can be recommended in particular for its presentation of model-based clustering. The book of[Frühwirth-Schnatter, 2006] can be recommended in particular for its focus on Bayesian inference.The editorial activity about mixture models is still important. We can cite the Handbook ofMixture Analysis by [Frühwirth-Schnatter et al., 2018] which presents a large overview of themethods and applications of mixture models. We can also mention the forthcoming monographyon model-based clustering [Bouveyron et al., 2019].The present special issue on mixture models deals with multiple aspects of this important fieldof research: clustering of dynamic networks, mixture of experts models, testing the number ofcomponets of univariate Gaussian mixtures, bootstrap procedures to assess the number of mixturecomponents, and an application in genomics. It is worthwhile to remark that all the articles of thisspecial issue are concerned with model selection and the crucial problem to choose a sensible andproper number of mixture components.Ricardo Rastelli considers the direct maximisation of the exact integrated completed likelihoodin a non informative setting for the Stochastic Block Model with dynamic networks.Faicel Chamroukhi and Bao-Tuyen Hyung propose regularised estimation and variable selectionprocedures for mixture of experts models to get parsimonious solutions.Didier Chauveau, Bernard Garel and Sophie Mercier go back to the basic problem of testingthe number of components in univariate Gaussian mixtures from a practical point of view.Zhivko Taushanov and André Berchtold propose different bootstrap procedures to select amixture model. They concentrate their illustrations on the Hidden Mixture Transition Distributionmodel for the clustering of longitudinal data.1 Inria Saclay-Île-de-France, Orsay, F-91405, FranceJournal de la Société Française de Statistique, Vol. 160 No. 1 33-34http://www.sfds.asso.fr/journal© Société Française de Statistique et Société Mathématique de France (2019) ISSN: 2102-623834 G. CeleuxChristine Keribin, Yi Lia, Tatiana Popova and Yves Rozenholc present an application ofmixture models on genomic data. They pay special attention to the selection of a relevant modeland illustrate the possible interest of the slope heuristics in the context they consider.I thank all the authors for their contributions and I hope that the readers of the Journal of theSFdS will be interested by this special issue.References[Bouveyron et al., 2019] Bouveyron, C., Celeux, G., Murphy, T. B., and Raftery, A. E. (2019). Model-based Clusteringand Classification for Data Science. Cambridge University Press. (Forthcoming).[Frühwirth-Schnatter, 2006] Frühwirth-Schnatter, S. (2006). Finite Mixture and Markov Switching Models. Springer-Verlag.[Frühwirth-Schnatter et al., 2018] Frühwirth-Schnatter, S., Celeux, G., and Robert, C. P. (2018). Handbook of MixtureAnalysis. CRC Press.[McLachlan and Peel, 2000] McLachlan, G. J. and Peel, D. (2000). Finite Mixture Models. John Wiley.[Titterington et al., 1985] Titterington, D. M., Smith, A. F. M., and Makov, U. E. (1985). Statistical Analysis of FiniteMixture distributions. John Wiley.Journal de la Société Française de Statistique, Vol. 160 No. 1 33-34http://www.sfds.asso.fr/journal© Société Française de Statistique et Société Mathématique de France (2019) ISSN: 2102-6238

Editorial of the Special Issue on Mixture Analysis

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Editorial of the Special Issue on Mixture Analysis

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Numérisation de Documents Anciens Mathématiques