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A Multiple-Try Extension of the Particle Marginal Metropolis-Hastings (PMMH) Algorithm with an Independent Proposal

Author

Listed:
  • Takashi Kamihigashi

    (Research Institute for Economics & Business Administration (RIEB), Kobe University, Japan)

  • Hiroyuki Watanabe

    (Research Institute for Economics & Business Administration (RIEB), Kobe University, Japan)

Abstract

In this paper we propose a multiple-try extension of the PMMH algorithm with an independent proposal. In our algorithm, I ∈ ℕ parameter particles are sampled from the independent proposal. For each of them, a particle fiter with K ∈ ℕ state particles is run. We show that the algorithm has the following properties: (i) the distribution of the Markov chain generated by the algorithm converges to the posterior of interest in total variation; (ii) as I increases to ∞, the acceptance probability at each iteration converges to 1; and (iii) as I increases to 1, the autocorrelation of any order for any parameter with bounded support converges to 0. These results indicate that the algorithm generates almost i.i.d. samples from the posterior for sufficiently large I. Our numerical experiments suggest that one can visibly improve mixing by increasing I from 1 to only 10. This does not significantly increase computation time if a computer with at least 10 threads is used.

Suggested Citation

  • Takashi Kamihigashi & Hiroyuki Watanabe, 2016. "A Multiple-Try Extension of the Particle Marginal Metropolis-Hastings (PMMH) Algorithm with an Independent Proposal," Discussion Paper Series DP2016-36, Research Institute for Economics & Business Administration, Kobe University.
    • Handle: RePEc:kob:dpaper:dp2016-36
    as

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    File URL: https://www.rieb.kobe-u.ac.jp/academic/ra/dp/English/DP2016-36.pdf
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    References listed on IDEAS

    as
    1. 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.
    2. 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.
    3. Geir Storvik, 2011. "On the Flexibility of Metropolis–Hastings Acceptance Probabilities in Auxiliary Variable Proposal Generation," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 38(2), pages 342-358, June.
    Full references (including those not matched with items on IDEAS)

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    More about this item

    Keywords

    Multiple-try method; Particle marginal Metropolis-Hastings; Markov chain Monte Carlo; Mixing; State space models;
    All these keywords.

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