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Fluctuations, stability and instability of a distributed particle filter with local exchange

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  • Heine, Kari
  • Whiteley, Nick

Abstract

We study a distributed particle filter proposed by Bolić et al. (2005). This algorithm involves m groups of M particles, with interaction between groups occurring through a “local exchange” mechanism. We establish a central limit theorem in the regime where M is fixed and m→∞. A formula we obtain for the asymptotic variance can be interpreted in terms of colliding Markov chains, enabling analytic and numerical evaluations of how the asymptotic variance behaves over time, with comparison to a benchmark algorithm consisting of m independent particle filters. We prove that subject to regularity conditions, when m is fixed both algorithms converge time-uniformly at rate M−1/2. Through use of our asymptotic variance formula we give counter-examples satisfying the same regularity conditions to show that when M is fixed neither algorithm, in general, converges time-uniformly at rate m−1/2.

Suggested Citation

  • Heine, Kari & Whiteley, Nick, 2017. "Fluctuations, stability and instability of a distributed particle filter with local exchange," Stochastic Processes and their Applications, Elsevier, vol. 127(8), pages 2508-2541.
    • Handle: RePEc:eee:spapps:v:127:y:2017:i:8:p:2508-2541
    DOI: 10.1016/j.spa.2016.11.003
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    References listed on IDEAS

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    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. Crisan, D. & Obanubi, O., 2012. "Particle filters with random resampling times," Stochastic Processes and their Applications, Elsevier, vol. 122(4), pages 1332-1368.
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    Cited by:

    1. Kari Heine & Nick Whiteley & A.Taylan Cemgil, 2020. "Parallelizing particle filters with butterfly interactions," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 47(2), pages 361-396, June.

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