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Sampling from Dirichlet process mixture models with unknown concentration parameter: mixing issues in large data

David I Hastie1, Silvia Liverani2, Sylvia Richardson3

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Statistics and Computing
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Summary
This summary is machine-generated.

We developed a Gibbs sampling algorithm for Dirichlet process mixture models. This method improves Markov chain Monte Carlo sampling efficiency, especially for large datasets and complex hierarchical models.

Keywords:
Bayesian clusteringDirichlet processMixture modelProfile regression

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Area of Science:

  • Statistics
  • Computational Statistics
  • Machine Learning

Background:

  • Dirichlet process mixture models are widely used for Bayesian nonparametrics.
  • Markov chain Monte Carlo (MCMC) sampling is crucial for inference in these models.
  • Efficient sampling is challenging, particularly for large datasets and complex models.

Purpose of the Study:

  • To introduce an efficient Gibbs sampling algorithm for general stick-breaking Dirichlet process mixture models.
  • To address challenges in MCMC sampling, including mixing and initialization sensitivity.
  • To develop methods for handling hierarchical extensions and label switching.

Main Methods:

  • Combining slice sampling (Walker, 2007) and retrospective sampling (Papaspiliopoulos & Roberts, 2008).
  • Implementing an open-source C++ software package within R, utilizing a blocking strategy.
  • Introducing a new label-switching move and computing the marginal partition posterior for hierarchical models.

Main Results:

  • Demonstrated good mixing behavior in MCMC samplers for large datasets.
  • Successfully implemented the algorithm in efficient open-source software.
  • Illustrated the method's effectiveness using a profile regression application with synthetic and real data.

Conclusions:

  • The proposed Gibbs sampling algorithm enhances MCMC efficiency for Dirichlet process mixture models.
  • The developed methods effectively address challenges in large-scale and hierarchical Bayesian inference.
  • The open-source implementation facilitates practical application in statistical modeling.