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Overfitting Bayesian Mixture Models with an Unknown Number of Components.

Zoé van Havre1, Nicole White2, Judith Rousseau3

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Summary
This summary is machine-generated.

This study introduces Zmix and Zswitch algorithms to accurately estimate finite mixture models, addressing overfitting and label switching issues in component number estimation. These methods improve Markov Chain Monte Carlo (MCMC) sampling for robust statistical analysis.

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Area of Science:

  • Statistics
  • Computational Statistics

Background:

  • Finite mixture models are widely used but face challenges with unknown component numbers.
  • Standard Markov Chain Monte Carlo (MCMC) methods exhibit mixing limitations.
  • Label switching is a persistent problem in mixture model estimation.

Purpose of the Study:

  • To propose novel algorithms for estimating finite mixture models with an unknown number of components.
  • To address non-identifiability from overfitting, MCMC mixing limitations, and label switching.
  • To provide a unified framework for robust mixture model estimation.

Main Methods:

  • An overfitting approach using the Zmix algorithm to estimate the number of components.
  • Prior parallel tempering implemented to enhance MCMC sampling efficiency.
  • A computationally light-weight method, Zswitch, for resolving label switching in overfitted mixtures.

Main Results:

  • Zmix accurately estimates the number of components and posterior parameters with sufficient sample size.
  • The approach reflects model uncertainty, reporting a range of candidate models and probabilities.
  • Zswitch effectively resolves label switching, leveraging allocation-based relabelling and loss functions.

Conclusions:

  • The Zmix and Zswitch algorithms offer robust solutions for finite mixture model estimation.
  • These methods, available in the R package Zmix, enhance MCMC sampling and address key estimation challenges.
  • The proposed techniques are applicable to univariate Gaussian mixture models.