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On a loss-based prior for the number of components in mixture models

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  • Grazian, Clara
  • Villa, Cristiano
  • Liseo, Brunero

Abstract

We introduce a prior distribution for the number of components of a mixture model. The prior considers the worth of each possible mixture, measured by a loss function with two components: one measures the loss in information in choosing the wrong mixture and one the loss due to complexity.

Suggested Citation

  • Grazian, Clara & Villa, Cristiano & Liseo, Brunero, 2020. "On a loss-based prior for the number of components in mixture models," Statistics & Probability Letters, Elsevier, vol. 158(C).
    • Handle: RePEc:eee:stapro:v:158:y:2020:i:c:s0167715219303025
    DOI: 10.1016/j.spl.2019.108656
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    References listed on IDEAS

    as
    1. Juárez, Miguel A. & Steel, Mark F. J., 2010. "Model-Based Clustering of Non-Gaussian Panel Data Based on Skew-t Distributions," Journal of Business & Economic Statistics, American Statistical Association, vol. 28(1), pages 52-66.
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    3. Cristiano Villa & Stephen Walker, 2015. "An Objective Bayesian Criterion to Determine Model Prior Probabilities," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 42(4), pages 947-966, December.
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    5. Mark S. Handcock & Adrian E. Raftery & Jeremy M. Tantrum, 2007. "Model‐based clustering for social networks," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 170(2), pages 301-354, March.
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    7. Ghosal,Subhashis & van der Vaart,Aad, 2017. "Fundamentals of Nonparametric Bayesian Inference," Cambridge Books, Cambridge University Press, number 9780521878265.
    8. Jeffrey W. Miller & Matthew T. Harrison, 2018. "Mixture Models With a Prior on the Number of Components," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 113(521), pages 340-356, January.
    9. Grazian, Clara & Robert, Christian P., 2018. "Jeffreys priors for mixture estimation: Properties and alternatives," Computational Statistics & Data Analysis, Elsevier, vol. 121(C), pages 149-163.
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