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Sequential quasi-Monte Carlo: Introduction for Non-Experts, Dimension Reduction, Application to Partly Observed Diffusion Processes

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  • Nicolas Chopin

    (CREST; ENSAE)

  • Mathieu Gerber

    (School of Mathematics, university of Bristol, University Walk, Clifton, Bristol)

Abstract

SMC (Sequential Monte Carlo) is a class of Monte Carlo algorithms for filtering and related sequential problems. [16] introduced SQMC (Sequential quasi-Monte Carlo), a QMC version of SMC. This paper has two objectives: (a) to introduce Sequential Monte Carlo to the QMC community, whose members are usually less familiar with state-space models and particle filtering; (b) to extend SQMC to the filtering of continuous-time state-space models, where the latent process is a diffusion. A recurring point in the paper will be the notion of dimension reduction, that is how to implement SQMC in such a way that it provides good performance despite the high dimension of the problem.

Suggested Citation

  • Nicolas Chopin & Mathieu Gerber, 2017. "Sequential quasi-Monte Carlo: Introduction for Non-Experts, Dimension Reduction, Application to Partly Observed Diffusion Processes," Working Papers 2017-35, Center for Research in Economics and Statistics.
    • Handle: RePEc:crs:wpaper:2017-35
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    References listed on IDEAS

    as
    1. Pierre Del Moral & Arnaud Doucet & Ajay Jasra, 2006. "Sequential Monte Carlo samplers," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 68(3), pages 411-436, June.
    2. Sangjoon Kim & Neil Shephard & Siddhartha Chib, 1998. "Stochastic Volatility: Likelihood Inference and Comparison with ARCH Models," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 65(3), pages 361-393.
    3. Neil Shephard & Siddhartha Chib & Olin School of Business & Washington University & Michael K. Pitt & Department of Economics & University of Warwick, 2004. "Likelihood based inference for diffusion driven models," Economics Series Working Papers 2004-FE-17, University of Oxford, Department of Economics.
    4. Siddhartha Chib & Michael K Pitt & Neil Shephard, 2004. "Likelihood based inference for diffusion driven models," Economics Papers 2004-W20, Economics Group, Nuffield College, University of Oxford.
    5. Mark Briers & Arnaud Doucet & Simon Maskell, 2010. "Smoothing algorithms for state–space models," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 62(1), pages 61-89, February.
    6. 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.
    7. Mathieu Gerber & Nicolas Chopin, 2015. "Sequential quasi Monte Carlo," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 77(3), pages 509-579, June.
    8. Nicolas Chopin, 2002. "A sequential particle filter method for static models," Biometrika, Biometrika Trust, vol. 89(3), pages 539-552, August.
    9. Pieralberto Guarniero & Adam M. Johansen & Anthony Lee, 2017. "The Iterated Auxiliary Particle Filter," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 112(520), pages 1636-1647, October.
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