IDEAS home Printed from https://ideas.repec.org/p/crs/wpaper/2010-34.html
   My bibliography  Save this paper

Free Energy Sequential Monte Carlo Application to Mixture Modelling

Author

Listed:
  • Nicolas Chopin

    (Crest)

  • Pierre Jacob

    (Crest)

Abstract

We introduce a new class of Sequential Monte Carlo (SMC) methods, whichwe call free energy SMC. This class is inspired by free energy methods, whichoriginate from Physics, and where one samples from a biased distribution suchthat a given function !(") of the state " is forced to be uniformly distributedover a given interval. From an initial sequence of distributions (#t) of interest,and a particular choice of !("), a free energy SMC sampler computes sequentiallya sequence of biased distributions (˜#t) with the following properties: (a)the marginal distribution of !(") with respect to ˜#t is approximatively uniformover a specified interval, and (b) ˜#t and #t have the same conditional distributionwith respect to !. We apply our methodology to mixture posteriordistributions, which are highly multimodal. In the mixture context, forcingcertain hyper-parameters to higher values greatly faciliates mode swapping,and makes it possible to recover a symetric output. We illustrate our approachwith univariate and bivariate Gaussian mixtures and two real-world datasets.

Suggested Citation

  • 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.
    • Handle: RePEc:crs:wpaper:2010-34
    as

    Download full text from publisher

    File URL: http://crest.science/RePEc/wpstorage/2010-34.pdf
    File Function: Crest working paper version
    Download Restriction: no
    ---><---

    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 & Tony Lelievre & Gabriel Stoltz, 2010. "Free Energy Methods for Efficient Exploration of Mixture Posterior Densities," Working Papers 2010-33, Center for Research in Economics and Statistics.
    3. 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.
    4. Nicolas Chopin, 2002. "A sequential particle filter method for static models," Biometrika, Biometrika Trust, vol. 89(3), pages 539-552, August.
    5. repec:dau:papers:123456789/1906 is not listed on IDEAS
    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. Drovandi, Christopher C. & Pettitt, Anthony N. & Henderson, Robert D. & McCombe, Pamela A., 2014. "Marginal reversible jump Markov chain Monte Carlo with application to motor unit number estimation," Computational Statistics & Data Analysis, Elsevier, vol. 72(C), pages 128-146.
    2. Garland Durham & John Geweke, 2013. "Adaptive Sequential Posterior Simulators for Massively Parallel Computing Environments," Working Paper Series 9, Economics Discipline Group, UTS Business School, University of Technology, Sydney.

    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. 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.
    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. 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.
    4. 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.
    5. 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.
    6. 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.
    7. 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.
    8. 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.
    9. Geweke, John & Durham, Garland, 2019. "Sequentially adaptive Bayesian learning algorithms for inference and optimization," Journal of Econometrics, Elsevier, vol. 210(1), pages 4-25.
    10. Arnaud Dufays, 2016. "Evolutionary Sequential Monte Carlo Samplers for Change-Point Models," Econometrics, MDPI, vol. 4(1), pages 1-33, March.
    11. Christian P. Robert, 2013. "Bayesian Computational Tools," Working Papers 2013-45, Center for Research in Economics and Statistics.
    12. T. -N. Nguyen & M. -N. Tran & R. Kohn, 2020. "Recurrent Conditional Heteroskedasticity," Papers 2010.13061, arXiv.org, revised Jan 2022.
    13. 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.
    14. 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.
    15. Fulop, Andras & Li, Junye, 2013. "Efficient learning via simulation: A marginalized resample-move approach," Journal of Econometrics, Elsevier, vol. 176(2), pages 146-161.
    16. 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.
    17. 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.
    18. 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).
    19. Li Ma, 2015. "Scalable Bayesian Model Averaging Through Local Information Propagation," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 110(510), pages 795-809, June.
    20. 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.

    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:crs:wpaper:2010-34. 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: Secretariat General (email available below). General contact details of provider: https://edirc.repec.org/data/crestfr.html .

    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.