IDEAS home Printed from https://ideas.repec.org/a/eee/stapro/v78y2008i17p3062-3069.html
   My bibliography  Save this article

Stability of sequential Monte Carlo samplers via the Foster-Lyapunov condition

Author

Listed:
  • Jasra, Ajay
  • Doucet, Arnaud

Abstract

Sequential Monte Carlo (SMC) samplers [Del Moral, P., Doucet, A., Jasra, A., 2006. Sequential Monte Carlo samplers. J. Roy. Statist. Soc. B 68, 411-436] are designed to simulate from a sequence of probability measures on a common measurable space . One way to measure the accuracy of the resulting Monte Carlo estimates is the asymptotic variance in the central limit theorem (CLT). We investigate the conditions, for algorithms used in practice, which are sufficient to ensure that the resulting expression is upper bounded, of which, the typical conditions (e.g. [Chopin, N., 2004. Central limit theorem for sequential Monte Carlo methods and its application to Bayesian inference. Ann. Statist. 32, 2385-2411]) are quite restrictive. We use the Foster-Lyapunov condition and contractions in the f-norm of the Markov kernels [Douc, R., Moulines, E., Rosenthal, J.S., 2004. Quantitative bounds on convergence of time-inhomogeneous Markov chains. Ann. Appl. Probab. 14, 1643-1665] to establish quantitative bounds on the asymptotic variance.

Suggested Citation

  • Jasra, Ajay & Doucet, Arnaud, 2008. "Stability of sequential Monte Carlo samplers via the Foster-Lyapunov condition," Statistics & Probability Letters, Elsevier, vol. 78(17), pages 3062-3069, December.
    • Handle: RePEc:eee:stapro:v:78:y:2008:i:17:p:3062-3069
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0167-7152(08)00268-X
    Download Restriction: Full text for ScienceDirect subscribers only
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    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. Nicolas Chopin, 2002. "Central Limit Theorem for Sequential Monte Carlo Methods and its Applications to Bayesian Inference," Working Papers 2002-44, Center for Research in Economics and Statistics.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Monica Billio & Roberto Casarin, 2010. "Identifying business cycle turning points with sequential Monte Carlo methods: an online and real-time application to the Euro area," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 29(1-2), pages 145-167.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Gareth W. Peters & Efstathios Panayi & Francois Septier, 2015. "SMC-ABC methods for the estimation of stochastic simulation models of the limit order book," Papers 1504.05806, arXiv.org.
    2. Targino, Rodrigo S. & Peters, Gareth W. & Shevchenko, Pavel V., 2015. "Sequential Monte Carlo Samplers for capital allocation under copula-dependent risk models," Insurance: Mathematics and Economics, Elsevier, vol. 61(C), pages 206-226.
    3. 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.
    4. Markku Lanne & Jani Luoto, 2015. "Estimation of DSGE Models under Diffuse Priors and Data-Driven Identification Constraints," CREATES Research Papers 2015-37, Department of Economics and Business Economics, Aarhus University.
    5. Derennes, Pierre & Morio, Jérôme & Simatos, Florian, 2021. "Simultaneous estimation of complementary moment independent and reliability-oriented sensitivity measures," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 182(C), pages 721-737.
    6. McKinley Trevelyan & Cook Alex R & Deardon Robert, 2009. "Inference in Epidemic Models without Likelihoods," The International Journal of Biostatistics, De Gruyter, vol. 5(1), pages 1-40, July.
    7. C. C. Drovandi & A. N. Pettitt, 2011. "Estimation of Parameters for Macroparasite Population Evolution Using Approximate Bayesian Computation," Biometrics, The International Biometric Society, vol. 67(1), pages 225-233, March.
    8. Sifat A Moon & Lee W Cohnstaedt & D Scott McVey & Caterina M Scoglio, 2019. "A spatio-temporal individual-based network framework for West Nile virus in the USA: Spreading pattern of West Nile virus," PLOS Computational Biology, Public Library of Science, vol. 15(3), pages 1-24, March.
    9. S. G. J. Senarathne & C. C. Drovandi & J. M. McGree, 2020. "Bayesian sequential design for Copula models," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 29(2), pages 454-478, June.
    10. Arnaud Dufays, 2016. "Evolutionary Sequential Monte Carlo Samplers for Change-Point Models," Econometrics, MDPI, vol. 4(1), pages 1-33, March.
    11. Fleischhacker, Jan, 2024. "Fiscal policy and the business cycle: An argument for non-linear policy rules," MPRA Paper 122497, University Library of Munich, Germany.
    12. Johansen, Adam M. & Doucet, Arnaud, 2008. "A note on auxiliary particle filters," Statistics & Probability Letters, Elsevier, vol. 78(12), pages 1498-1504, September.
    13. Axel Finke & Adam Johansen & Dario Spanò, 2014. "Static-parameter estimation in piecewise deterministic processes using particle Gibbs samplers," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 66(3), pages 577-609, June.
    14. James Martin & Ajay Jasra & Emma McCoy, 2013. "Inference for a class of partially observed point process models," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 65(3), pages 413-437, June.
    15. Li, Dan & Clements, Adam & Drovandi, Christopher, 2021. "Efficient Bayesian estimation for GARCH-type models via Sequential Monte Carlo," Econometrics and Statistics, Elsevier, vol. 19(C), pages 22-46.
    16. Fulop, Andras & Li, Junye, 2013. "Efficient learning via simulation: A marginalized resample-move approach," Journal of Econometrics, Elsevier, vol. 176(2), pages 146-161.
    17. Mark Bognanni & John Zito, 2019. "Sequential Bayesian Inference for Vector Autoregressions with Stochastic Volatility," Working Papers 19-29, Federal Reserve Bank of Cleveland.
    18. McGree, J.M., 2017. "Developments of the total entropy utility function for the dual purpose of model discrimination and parameter estimation in Bayesian design," Computational Statistics & Data Analysis, Elsevier, vol. 113(C), pages 207-225.
    19. Hoang Nguyen & Trong-Nghia Nguyen & Minh-Ngoc Tran, 2023. "A dynamic leverage stochastic volatility model," Applied Economics Letters, Taylor & Francis Journals, vol. 30(1), pages 97-102, January.
    20. Warne, David J. & Baker, Ruth E. & Simpson, Matthew J., 2018. "Multilevel rejection sampling for approximate Bayesian computation," Computational Statistics & Data Analysis, Elsevier, vol. 124(C), pages 71-86.

    More about this item

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:stapro:v:78:y:2008:i:17:p:3062-3069. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/wps/find/journaldescription.cws_home/622892/description#description .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.