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Dealing with label switching in mixture models under genuine multimodality

  • Grn, Bettina
  • Leisch, Friedrich
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    The fitting of finite mixture models is an ill-defined estimation problem, as completely different parameterizations can induce similar mixture distributions. This leads to multiple modes in the likelihood, which is a problem for frequentist maximum likelihood estimation, and complicates statistical inference of Markov chain Monte Carlo draws in Bayesian estimation. For the analysis of the posterior density of these draws, a suitable separation into different modes is desirable. In addition, a unique labelling of the component specific estimates is necessary to solve the label switching problem. This paper presents and compares two approaches to achieve these goals: relabelling under multimodality and constrained clustering. The algorithmic details are discussed, and their application is demonstrated on artificial and real-world data.

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    Article provided by Elsevier in its journal Journal of Multivariate Analysis.

    Volume (Year): 100 (2009)
    Issue (Month): 5 (May)
    Pages: 851-861

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    Handle: RePEc:eee:jmvana:v:100:y:2009:i:5:p:851-861
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    1. Leisch, Friedrich, 2006. "A toolbox for K-centroids cluster analysis," Computational Statistics & Data Analysis, Elsevier, vol. 51(2), pages 526-544, November.
    2. Chung H. & Loken E. & Schafer J.L., 2004. "Difficulties in Drawing Inferences With Finite-Mixture Models: A Simple Example With a Simple Solution," The American Statistician, American Statistical Association, vol. 58, pages 152-158, May.
    3. Matthew Stephens, 2000. "Dealing with label switching in mixture models," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 62(4), pages 795-809.
    4. Lawrence Hubert & Phipps Arabie, 1985. "Comparing partitions," Journal of Classification, Springer, vol. 2(1), pages 193-218, December.
    5. Marin, Jean-Michel & Mengersen, Kerrie & Robert, Christian P., 2005. "Bayesian Modelling and Inference on Mixtures of Distributions," Economics Papers from University Paris Dauphine 123456789/6069, Paris Dauphine University.
    6. Michael Brusco & J. Cradit, 2001. "A variable-selection heuristic for K-means clustering," Psychometrika, Springer, vol. 66(2), pages 249-270, June.
    7. Hardy, Andre, 1996. "On the number of clusters," Computational Statistics & Data Analysis, Elsevier, vol. 23(1), pages 83-96, November.
    8. Jerome H. Friedman & Jacqueline J. Meulman, 2004. "Clustering objects on subsets of attributes (with discussion)," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 66(4), pages 815-849.
    9. Robert Tibshirani & Guenther Walther & Trevor Hastie, 2001. "Estimating the number of clusters in a data set via the gap statistic," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 63(2), pages 411-423.
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