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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. 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.
    2. repec:dau:papers:123456789/6069 is not listed on IDEAS
    3. Ghosal,Subhashis & van der Vaart,Aad, 2017. "Fundamentals of Nonparametric Bayesian Inference," Cambridge Books, Cambridge University Press, number 9780521878265, October.
    4. 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.
    5. 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.
    6. 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.
    7. Sylvia. Richardson & Peter J. Green, 1997. "On Bayesian Analysis of Mixtures with an Unknown Number of Components (with discussion)," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 59(4), pages 731-792.
    8. 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.
    9. repec:dau:papers:123456789/4648 is not listed on IDEAS
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