IDEAS home Printed from https://ideas.repec.org/a/eee/csdana/v93y2016icp246-254.html
   My bibliography  Save this article

Transdimensional sequential Monte Carlo using variational Bayes — SMCVB

Author

Listed:
  • McGrory, C.A.
  • Pettitt, A.N.
  • Titterington, D.M.
  • Alston, C.L.
  • Kelly, M.

Abstract

A new transdimensional Sequential Monte Carlo (SMC) algorithm called SMCVB is proposed. In an SMC approach, a weighted sample of particles is generated from a sequence of probability distributions which ‘converge’ to the target distribution of interest, in this case a Bayesian posterior distribution. The approach is based on the use of variational Bayes to propose new particles at each iteration of the SMCVB algorithm in order to target the posterior more efficiently. The variational-Bayes-generated proposals are not limited to a fixed dimension. This means that the weighted particle sets that arise can have varying dimensions thereby allowing us the option to also estimate an appropriate dimension for the model. This novel algorithm is outlined within the context of finite mixture model estimation. This provides a less computationally demanding alternative to using reversible jump Markov chain Monte Carlo kernels within an SMC approach. We illustrate these ideas in a simulated data analysis and in applications.

Suggested Citation

  • McGrory, C.A. & Pettitt, A.N. & Titterington, D.M. & Alston, C.L. & Kelly, M., 2016. "Transdimensional sequential Monte Carlo using variational Bayes — SMCVB," Computational Statistics & Data Analysis, Elsevier, vol. 93(C), pages 246-254.
    • Handle: RePEc:eee:csdana:v:93:y:2016:i:c:p:246-254
    DOI: 10.1016/j.csda.2015.03.006
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0167947315000742
    Download Restriction: Full text for ScienceDirect subscribers only.
    File URL: https://libkey.io/10.1016/j.csda.2015.03.006?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    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. Sylvia. Richardson & Peter J. Green, 1997. "On Bayesian Analysis of Mixtures with an Unknown Number of Components (with discussion)," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 59(4), pages 731-792.
    3. McGrory, C.A. & Titterington, D.M., 2007. "Variational approximations in Bayesian model selection for finite mixture distributions," Computational Statistics & Data Analysis, Elsevier, vol. 51(11), pages 5352-5367, July.
    4. Nicolas Chopin, 2002. "A sequential particle filter method for static models," Biometrika, Biometrika Trust, vol. 89(3), pages 539-552, August.
    5. Jasra, Ajay & Doucet, Arnaud & Stephens, David A. & Holmes, Christopher C., 2008. "Interacting sequential Monte Carlo samplers for trans-dimensional simulation," Computational Statistics & Data Analysis, Elsevier, vol. 52(4), pages 1765-1791, January.
    6. Ormerod, J. T. & Wand, M. P., 2010. "Explaining Variational Approximations," The American Statistician, American Statistical Association, vol. 64(2), pages 140-153.
    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. Han, Ningren & Ram, Rajeev J., 2020. "Bayesian modeling and computation for analyte quantification in complex mixtures using Raman spectroscopy," Computational Statistics & Data Analysis, Elsevier, vol. 143(C).

    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. Geweke, John & Durham, Garland, 2019. "Sequentially adaptive Bayesian learning algorithms for inference and optimization," Journal of Econometrics, Elsevier, vol. 210(1), pages 4-25.
    2. Jasra, Ajay & Doucet, Arnaud & Stephens, David A. & Holmes, Christopher C., 2008. "Interacting sequential Monte Carlo samplers for trans-dimensional simulation," Computational Statistics & Data Analysis, Elsevier, vol. 52(4), pages 1765-1791, January.
    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. Nicolas Chopin & Pierre Jacob, 2010. "Free Energy Sequential Monte Carlo Application to Mixture Modelling," Working Papers 2010-34, Center for Research in Economics and Statistics.
    5. 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.
    6. Xiaohong Chen & Timothy M. Christensen & Elie Tamer, 2018. "Monte Carlo Confidence Sets for Identified Sets," Econometrica, Econometric Society, vol. 86(6), pages 1965-2018, November.
    7. 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.
    8. Edward Herbst & Frank Schorfheide, 2014. "Sequential Monte Carlo Sampling For Dsge Models," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 29(7), pages 1073-1098, November.
    9. 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.
    10. Lau, F. Din-Houn & Gandy, Axel, 2014. "RMCMC: A system for updating Bayesian models," Computational Statistics & Data Analysis, Elsevier, vol. 80(C), pages 99-110.
    11. Gholamreza Hajargasht & William E. Griffiths, 2018. "Estimation and testing of stochastic frontier models using variational Bayes," Journal of Productivity Analysis, Springer, vol. 50(1), pages 1-24, October.
    12. Arnaud Dufays, 2016. "Evolutionary Sequential Monte Carlo Samplers for Change-Point Models," Econometrics, MDPI, vol. 4(1), pages 1-33, March.
    13. Christian P. Robert, 2013. "Bayesian Computational Tools," Working Papers 2013-45, Center for Research in Economics and Statistics.
    14. T. -N. Nguyen & M. -N. Tran & R. Kohn, 2020. "Recurrent Conditional Heteroskedasticity," Papers 2010.13061, arXiv.org, revised Jan 2022.
    15. 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.
    16. 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.
    17. Fulop, Andras & Li, Junye, 2013. "Efficient learning via simulation: A marginalized resample-move approach," Journal of Econometrics, Elsevier, vol. 176(2), pages 146-161.
    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. Drovandi, Christopher C. & McGree, James M. & Pettitt, Anthony N., 2013. "Sequential Monte Carlo for Bayesian sequentially designed experiments for discrete data," Computational Statistics & Data Analysis, Elsevier, vol. 57(1), pages 320-335.
    20. Zhang, Jinyu & Zhang, Qiaosen & Li, Yong & Wang, Qianchao, 2023. "Sequential Bayesian inference for agent-based models with application to the Chinese business cycle," Economic Modelling, Elsevier, vol. 126(C).

    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:csdana:v:93:y:2016:i:c:p:246-254. 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/locate/csda .

    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.