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Waste‐free sequential Monte Carlo

Author

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  • Hai‐Dang Dau
  • Nicolas Chopin

Abstract

A standard way to move particles in a sequential Monte Carlo (SMC) sampler is to apply several steps of a Markov chain Monte Carlo (MCMC) kernel. Unfortunately, it is not clear how many steps need to be performed for optimal performance. In addition, the output of the intermediate steps are discarded and thus wasted somehow. We propose a new, waste‐free SMC algorithm which uses the outputs of all these intermediate MCMC steps as particles. We establish that its output is consistent and asymptotically normal. We use the expression of the asymptotic variance to develop various insights on how to implement the algorithm in practice. We develop in particular a method to estimate, from a single run of the algorithm, the asymptotic variance of any particle estimate. We show empirically, through a range of numerical examples, that waste‐free SMC tends to outperform standard SMC samplers, and especially so in situations where the mixing of the considered MCMC kernels decreases across iterations (as in tempering or rare event problems).

Suggested Citation

  • Hai‐Dang Dau & Nicolas Chopin, 2022. "Waste‐free sequential Monte Carlo," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 84(1), pages 114-148, February.
    • Handle: RePEc:bla:jorssb:v:84:y:2022:i:1:p:114-148
    DOI: 10.1111/rssb.12475
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    References listed on IDEAS

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    4. Nicolas Chopin, 2002. "A sequential particle filter method for static models," Biometrika, Biometrika Trust, vol. 89(3), pages 539-552, August.
    5. 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.
    6. A Lee & N Whiteley, 2018. "Variance estimation in the particle filter," Biometrika, Biometrika Trust, vol. 105(3), pages 609-625.
    7. Beskos, Alexandros & Jasra, Ajay & Law, Kody & Tempone, Raul & Zhou, Yan, 2017. "Multilevel sequential Monte Carlo samplers," Stochastic Processes and their Applications, Elsevier, vol. 127(5), pages 1417-1440.
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