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Efficient Sequential Monte Carlo With Multiple Proposals and Control Variates

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  • Wentao Li
  • Rong Chen
  • Zhiqiang Tan

Abstract

Sequential Monte Carlo is a useful simulation-based method for online filtering of state-space models. For certain complex state-space models, a single proposal distribution is usually not satisfactory and using multiple proposal distributions is a general approach to address various aspects of the filtering problem. This article proposes an efficient method of using multiple proposals in combination with control variates. The likelihood approach of Tan (2004) is used in both resampling and estimation. The new algorithm is shown to be asymptotically more efficient than the direct use of multiple proposals and control variates. The guidance for selecting multiple proposals and control variates is also given. Numerical examples are used to demonstrate that the new algorithm can significantly improve over the bootstrap filter and auxiliary particle filter.

Suggested Citation

  • Wentao Li & Rong Chen & Zhiqiang Tan, 2016. "Efficient Sequential Monte Carlo With Multiple Proposals and Control Variates," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 111(513), pages 298-313, March.
    • Handle: RePEc:taf:jnlasa:v:111:y:2016:i:513:p:298-313
    DOI: 10.1080/01621459.2015.1006364
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    1. Shephard, Neil (ed.), 2005. "Stochastic Volatility: Selected Readings," OUP Catalogue, Oxford University Press, number 9780199257201.
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    Cited by:

    1. Chris J. Oates & Mark Girolami & Nicolas Chopin, 2017. "Control functionals for Monte Carlo integration," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 79(3), pages 695-718, June.
    2. Crucinio, Francesca R. & Johansen, Adam M., 2023. "Properties of marginal sequential Monte Carlo methods," Statistics & Probability Letters, Elsevier, vol. 203(C).

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