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A sequential smoothing algorithm with linear computational cost

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  • Paul Fearnhead
  • David Wyncoll
  • Jonathan Tawn

Abstract

In this paper we propose a new particle smoother that has a computational complexity of O(N), where N is the number of particles. This compares favourably with the O(N-super-2) computational cost of most smoothers. The new method also overcomes some degeneracy problems in existing algorithms. Through simulation studies we show that substantial gains in efficiency are obtained for practical amounts of computational cost. It is shown both through these simulation studies, and by the analysis of an athletics dataset, that our new method also substantially outperforms the simple filter-smoother, the only other smoother with computational cost that is O(N). Copyright 2010, Oxford University Press.

Suggested Citation

  • Paul Fearnhead & David Wyncoll & Jonathan Tawn, 2010. "A sequential smoothing algorithm with linear computational cost," Biometrika, Biometrika Trust, vol. 97(2), pages 447-464.
    • Handle: RePEc:oup:biomet:v:97:y:2010:i:2:p:447-464
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    File URL: http://hdl.handle.net/10.1093/biomet/asq013
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    Citations

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    Cited by:

    1. Jimmy Olsson & Johan Westerborn Alenlöv, 2020. "Particle-based online estimation of tangent filters with application to parameter estimation in nonlinear state-space models," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 72(2), pages 545-576, April.
    2. Persing, Adam & Jasra, Ajay, 2013. "Likelihood computation for hidden Markov models via generalized two-filter smoothing," Statistics & Probability Letters, Elsevier, vol. 83(5), pages 1433-1442.
    3. repec:wyi:journl:002173 is not listed on IDEAS
    4. Fredrik Lindsten & Randal Douc & Eric Moulines, 2015. "Uniform Ergodicity of the Particle Gibbs Sampler," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 42(3), pages 775-797, September.
    5. Scharth, Marcel & Kohn, Robert, 2016. "Particle efficient importance sampling," Journal of Econometrics, Elsevier, vol. 190(1), pages 133-147.
    6. Genshiro Kitagawa, 2014. "Computational aspects of sequential Monte Carlo filter and smoother," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 66(3), pages 443-471, June.
    7. Parfait Munezero, 2022. "Efficient particle smoothing for Bayesian inference in dynamic survival models," Computational Statistics, Springer, vol. 37(2), pages 975-994, April.
    8. António A. F. Santos, 2015. "On the Forecasting of Financial Volatility Using Ultra-High Frequency Data," GEMF Working Papers 2015-17, GEMF, Faculty of Economics, University of Coimbra.
    9. Deschamps, P., 2015. "Alternative Formulation of the Leverage Effect in a Stochastic Volatility Model with Asymmetric Heavy-Tailed Errors," LIDAM Discussion Papers CORE 2015020, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    10. Gangloff, Hugo & Morales, Katherine & Petetin, Yohan, 2023. "Deep parameterizations of pairwise and triplet Markov models for unsupervised classification of sequential data," Computational Statistics & Data Analysis, Elsevier, vol. 180(C).

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