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On the Particle Gibbs Sampler

Author

Listed:
  • Nicolas Chopin

    () (CREST)

  • Sumeetpal S. Singh

    () (Cambridge University)

Abstract

The particle Gibbs sampler is a Markov chain Monte Carlo (MCMC) algorithm which operates on the extended space of the auxiliary variables generated by an interacting particle system. In particular, it samples the discrete variables that determine the particle genealogy. We propose a coupling construction between two particle Gibbs updates from different starting points, which is such that the coupling probability may be made arbitrary large by taking the particle system large enough. A direct consequence of this result is the uniform ergodicity of the Particle Gibbs Markov kernel. We discuss several algorithmic variations of Particle Gibbs, either proposed in the literature or original. For some of these variants we are able to prove that they dominate the original algorithm in asymptotic efficiency as measured by the variance of the central limit theorem's limiting distribution. A detailed numerical study is provided to demonstrate the efficacy of Particle Gibbs and the proposed variants

Suggested Citation

  • Nicolas Chopin & Sumeetpal S. Singh, 2013. "On the Particle Gibbs Sampler," Working Papers 2013-41, Center for Research in Economics and Statistics.
  • Handle: RePEc:crs:wpaper:2013-41
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    References listed on IDEAS

    as
    1. Christophe Andrieu & Arnaud Doucet & Roman Holenstein, 2010. "Particle Markov chain Monte Carlo methods," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 72(3), pages 269-342.
    2. repec:dau:papers:123456789/7305 is not listed on IDEAS
    3. Pitt, Michael K. & Silva, Ralph dos Santos & Giordani, Paolo & Kohn, Robert, 2012. "On some properties of Markov chain Monte Carlo simulation methods based on the particle filter," Journal of Econometrics, Elsevier, vol. 171(2), pages 134-151.
    4. N. Chopin & P. E. Jacob & O. Papaspiliopoulos, 2013. "SMC-super-2: an efficient algorithm for sequential analysis of state space models," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 75(3), pages 397-426, June.
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    Cited by:

    1. Creal, Drew D. & Tsay, Ruey S., 2015. "High dimensional dynamic stochastic copula models," Journal of Econometrics, Elsevier, vol. 189(2), pages 335-345.
    2. Patrick Leung & Catherine S. Forbes & Gael M. Martin & Brendan McCabe, 2016. "Data-driven particle Filters for particle Markov Chain Monte Carlo," Monash Econometrics and Business Statistics Working Papers 17/16, Monash University, Department of Econometrics and Business Statistics.
    3. Axel Finke & Adam Johansen & Dario Spanò, 2014. "Static-parameter estimation in piecewise deterministic processes using particle Gibbs samplers," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 66(3), pages 577-609, June.

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