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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, June.
    2. 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.
    3. repec:dau:papers:123456789/7305 is not listed on IDEAS
    4. 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.
    Full references (including those not matched with items on IDEAS)

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    Cited by:

    1. Mengheng Li & Marcel Scharth, 2022. "Leverage, Asymmetry, and Heavy Tails in the High-Dimensional Factor Stochastic Volatility Model," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 40(1), pages 285-301, January.
    2. Bournakis, Ioannis & Tsionas, Mike G., 2023. "A Non-Parametric Estimation of Productivity with Idiosyncratic and Aggregate Shocks: The Role of Research and Development (R&D) and Corporate Tax," MPRA Paper 118100, University Library of Munich, Germany.
    3. Tsionas, Mike G. & Mallick, Sushanta K., 2019. "A Bayesian semiparametric approach to stochastic frontiers and productivity," European Journal of Operational Research, Elsevier, vol. 274(1), pages 391-402.
    4. Creal, Drew D. & Tsay, Ruey S., 2015. "High dimensional dynamic stochastic copula models," Journal of Econometrics, Elsevier, vol. 189(2), pages 335-345.
    5. Tsionas, Mike G., 2022. "Convex non-parametric least squares, causal structures and productivity," European Journal of Operational Research, Elsevier, vol. 303(1), pages 370-387.
    6. Mike G. Tsionas & Subal C. Kumbhakar, 2023. "Productivity and Performance: A GMM approach," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 85(2), pages 331-344, April.
    7. Tsionas, Mike G., 2020. "On a model of environmental performance and technology gaps," European Journal of Operational Research, Elsevier, vol. 285(3), pages 1141-1152.
    8. Emmanuel C. Mamatzakis & Steven Ongena & Mike G. Tsionas, 2023. "The response of household debt to COVID-19 using a neural networks VAR in OECD," Empirical Economics, Springer, vol. 65(1), pages 65-91, July.
    9. 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.
    10. 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.
    11. Mike G. Tsionas & Nicholas Apergis, 2023. "Another look at contagion across United States and European financial markets: Evidence from the credit default swaps markets," International Journal of Finance & Economics, John Wiley & Sons, Ltd., vol. 28(1), pages 1137-1155, January.

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