Quotation Malsiner-Walli, Gertraud, Frühwirth-Schnatter, Sylvia, Grün, Bettina. 2017. Identifying mixtures of mixtures using Bayesian estimation. Journal of Computational and Graphical Statistics. 26 (2), 285-295.




The use of a finite mixture of normal distributions in model-based clustering allows us to capture non-Gaussian data clusters. However, identifying the clusters from the normal components is challenging and in general either achieved by imposing constraints on the model or by using post-processing procedures. Within the Bayesian framework, we propose a different approach based on sparse finite mixtures to achieve identifiability. We specify a hierarchical prior, where the hyperparameters are carefully selected such that they are reflective of the cluster structure aimed at. In addition, this prior allows us to estimate the model using standard MCMC sampling methods. In combination with a post-processing approach which resolves the label switching issue and results in an identified model, our approach allows us to simultaneously (1) determine the number of clusters, (2) flexibly approximate the cluster distributions in a semiparametric way using finite mixtures of normals and (3) identify cluster-specific parameters and classify observations. The proposed approach is illustrated in two simulation studies and on benchmark datasets. Supplementary materials for this article are available online.


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Publication's profile

Status of publication Published
Affiliation WU
Type of publication Journal article
Journal Journal of Computational and Graphical Statistics
Citation Index SCI
WU-Journal-Rating new FIN-A, VW-C
Language English
Title Identifying mixtures of mixtures using Bayesian estimation
Volume 26
Number 2
Year 2017
Page from 285
Page to 295
Reviewed? Y
URL http://www.tandfonline.com/doi/full/10.1080/10618600.2016.1200472
DOI http://dx.doi.org/10.1080/10618600.2016.1200472
Open Access Y
Open Access Link http://dx.doi.org/10.1080/10618600.2016.1200472


Malsiner-Walli, Gertraud (Details)
Frühwirth-Schnatter, Sylvia (Details)
Grün, Bettina (Details)
Institute for Statistics and Mathematics IN (Details)
Research areas (ÖSTAT Classification 'Statistik Austria')
1105 Computer software (Details)
1113 Mathematical statistics (Details)
1162 Statistics (Details)
5701 Applied statistics (Details)
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