The label switching problem in mixture models

Authors

  • Ali Etemad Department of Mathematics, Urmia University, Urmia, Iran
  • Gholamhossein Gholami Department of Statistics, University of Mazandaran, Babolsar, Iran
  • Hamideh Rasi Department of Mathematics, Tabriz University, Tabriz, Iran

Keywords:

Mixture Models, Label Switching, Identi

Abstract

Mixture models are fascinating objects in that, while based on elementary distributions, they of-fer a much wider range of modeling possibilities than their components. They also need both highlycomplex computational challenges and delicate inferential derivations . In Bayesian framework thiskind of models do not admit an analytical solution and one should content him/her self by an ap-proximative solution.In this work, we introduce denition of identiability in statistical model. We focus on denition ofidentiability of mixtures of models from Bayesian point of view. This issue is called label-switchingproblem in Bayesian literatures. We will study a method to identify the mixtures parameter by usingMCMC output.

References

Jean-Michel, M., Christian, P., 2007. Robert, Bayesian core: A practical approach to computational

Bayesian statistics, Springer.

Prakasa Rao, B.L.S., 1992. Identifiability in Stochastic Models, Academic Press.

Sylvia Frühwirth-Schnatter., 2006. Finite Mixture and Markov Switching Models, Springer.

Sylvia Frühwirth-Schnatter., 2010. Bayesian inference for finite mixtures of univariate and multivariate

skew-normal and skew-t distributions, Biostatistics., 11,2, pp.317–336.

Sasra, A., Holmes, C.C., Stephens, D.A., 2005. MCMC Methods and the Label Switching Problem in

Bayesian Mixture Modeling. Statist. sci., 20, 50-67.

Geoffrey McLachlan., David PEEL, Finite Mixture Models., 2004. Wiley series in probability and statistics .

CHANG, ILSUNG., 2005. Bayesian inference on mixture models and their applications, Texas A&M

University, 74–80.

RICHARD GERLACH., 2000. Chris Carter and Robert KOHN, Efficient Bayesian Inference for Dynamic

Mixture Models. J. Amer. Statist. Associat., Vol. 95, No. 451, Sep pp . 819–828.

Berkhof, J., Van Michelin, I., Gelman, A., 2003. A Bayesian Approach to the Selection and Testing of

Mixture Models. Statist. Sin., 13:423-442.

Casella, Robert, C., Wells, M., 2004. Mixture Models, latent Variable and Partitioned Importance

Sampling. Statist. Methodol., 1, 1-18.

Dieboit, J., 1994. Robert , Estimation of Finite Mixture Distribution by Bayesian Sampling. J. Royal Statist.

Soc. Series., B,56, 363-375

Published

2020-09-06

How to Cite

Etemad, A. ., Gholami, G. ., & Rasi, H. . (2020). The label switching problem in mixture models. Scientific Journal of Pure and Applied Sciences, 3(7), 617-621. Retrieved from http://sjournals.com/index.php/sjpas/article/view/824

Issue

Section

Mathematics

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