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Allocation Variable-Based Probabilistic Algorithm to Deal with Label Switching Problem in Bayesian Mixture Models.

Jia-Chiun Pan1, Chih-Min Liu2, Hai-Gwo Hwu2

  • 1Department of Mathematics, National Chung Cheng University, Chiayi, Taiwan.

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|October 13, 2015
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Summary
This summary is machine-generated.

A new allocation variable-based (AVP) probabilistic algorithm addresses the label switching problem in Bayesian mixture models. This method effectively relabels posterior samples, demonstrating success in simulations and real-world data analysis.

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Area of Science:

  • Statistics
  • Computational Statistics
  • Bayesian Inference

Background:

  • The Bayesian approach to mixture models can suffer from label switching due to nonidentifiable posterior distributions.
  • This issue arises from permutations of component labels, complicating parameter estimation.

Purpose of the Study:

  • To propose a novel probabilistic relabelling algorithm to solve the label switching problem in mixture models.
  • To establish a model for the posterior distribution of allocation variables, incorporating the label switching phenomenon.

Main Methods:

  • Developed an allocation variable-based (AVP) probabilistic relabelling approach for fixed and known numbers of components.
  • Modeled the posterior distribution of allocation variables to account for label switching.
  • Stochastically relabeled posterior samples using the established posterior probabilities.

Main Results:

  • The AVP algorithm successfully addresses the label switching problem in mixture models.
  • Simulation studies demonstrated the effectiveness of the AVP algorithm compared to existing methods.
  • The proposed approach was validated on a real-world dataset.

Conclusions:

  • The AVP algorithm offers a robust solution for the label switching problem in Bayesian mixture models.
  • This method enhances the reliability of parameter estimation in mixture models.
  • The study confirms the practical applicability and superiority of the AVP approach.