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Quantifying the uncertainty of partitions for infinite mixture models

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  • Lavigne, Aurore
  • Liverani, Silvia

Abstract

Bayesian clustering models, such as Dirichlet process mixture models (DPMMs), are sophisticated flexible models. They induce a posterior distribution on the set of all partitions of a set of observations. Analysing this posterior distribution is of great interest, but it comes with several challenges. First of all, the number of partitions is overwhelmingly large even for moderate values of the number of observations. Consequently the sample space of the posterior distribution of the partitions is not explored well by MCMC samplers. Second, due to the complexity of representing the uncertainty of partitions, usually only maximum a posteriori estimates of the posterior distribution of partitions are provided and discussed in the literature. In this paper we propose a numerical and graphical method for quantifying the uncertainty of the clusters of a given partition of the data and we suggest how this tool can be used to learn about the partition uncertainty.

Suggested Citation

  • Lavigne, Aurore & Liverani, Silvia, 2024. "Quantifying the uncertainty of partitions for infinite mixture models," Statistics & Probability Letters, Elsevier, vol. 204(C).
    • Handle: RePEc:eee:stapro:v:204:y:2024:i:c:s0167715223001542
    DOI: 10.1016/j.spl.2023.109930
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    References listed on IDEAS

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    1. Silvia Liverani & Lucy Leigh & Irene L. Hudson & Julie E. Byles, 2021. "Clustering method for censored and collinear survival data," Computational Statistics, Springer, vol. 36(1), pages 35-60, March.
    2. Liverani, Silvia & Hastie, David I. & Azizi, Lamiae & Papathomas, Michail & Richardson, Sylvia, 2015. "PReMiuM: An R Package for Profile Regression Mixture Models Using Dirichlet Processes," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 64(i07).
    3. Christian Hennig, 2010. "Methods for merging Gaussian mixture components," Advances in Data Analysis and Classification, Springer;German Classification Society - Gesellschaft für Klassifikation (GfKl);Japanese Classification Society (JCS);Classification and Data Analysis Group of the Italian Statistical Society (CLADAG);International Federation of Classification Societies (IFCS), vol. 4(1), pages 3-34, April.
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