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Stopping‐time resampling for sequential Monte Carlo methods

Author

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  • Yuguo Chen
  • Junyi Xie
  • Jun S. Liu

Abstract

Summary. Motivated by the statistical inference problem in population genetics, we present a new sequential importance sampling with resampling strategy. The idea of resampling is key to the recent surge of popularity of sequential Monte Carlo methods in the statistics and engin‐eering communities, but existing resampling techniques do not work well for coalescent‐based inference problems in population genetics. We develop a new method called ‘stopping‐time resampling’, which allows us to compare partially simulated samples at different stages to terminate unpromising partial samples and to multiply promising samples early on. To illustrate the idea, we first apply the new method to approximate the solution of a Dirichlet problem and the likelihood function of a non‐Markovian process. Then we focus on its application in population genetics. All our examples show that the new resampling method can significantly improve the computational efficiency of existing sequential importance sampling methods.

Suggested Citation

  • Yuguo Chen & Junyi Xie & Jun S. Liu, 2005. "Stopping‐time resampling for sequential Monte Carlo methods," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 67(2), pages 199-217, April.
    • Handle: RePEc:bla:jorssb:v:67:y:2005:i:2:p:199-217
    DOI: 10.1111/j.1467-9868.2005.00497.x
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    Cited by:

    1. Radislav Vaisman & Ofer Strichman & Ilya Gertsbakh, 2015. "Model Counting of Monotone Conjunctive Normal Form Formulas with Spectra," INFORMS Journal on Computing, INFORMS, vol. 27(2), pages 406-415, May.
    2. Drew Creal, 2012. "A Survey of Sequential Monte Carlo Methods for Economics and Finance," Econometric Reviews, Taylor & Francis Journals, vol. 31(3), pages 245-296.
    3. Clemens Draxler, 2018. "Bayesian conditional inference for Rasch models," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 102(2), pages 245-262, April.
    4. Bartolucci, Francesco & Pigini, Claudia & Valentini, Francesco, 2021. "MCMC Conditional Maximum Likelihood for the two-way fixed-effects logit," MPRA Paper 110034, University Library of Munich, Germany.
    5. 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.
    6. Ian Dinwoodie & Kruti Pandya, 2015. "Exact tests for singular network data," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 67(4), pages 687-706, August.
    7. Sanda Micula, 2015. "Statistical Computer Simulations And Monte Carlo Methods," Romanian Economic Business Review, Romanian-American University, vol. 9(2), pages 384-394, December.
    8. Andrew C. Titman & Linda D. Sharples, 2010. "Semi-Markov Models with Phase-Type Sojourn Distributions," Biometrics, The International Biometric Society, vol. 66(3), pages 742-752, September.
    9. Radislav Vaisman & Dirk P. Kroese, 2017. "Stochastic Enumeration Method for Counting Trees," Methodology and Computing in Applied Probability, Springer, vol. 19(1), pages 31-73, March.

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