IDEAS home Printed from https://ideas.repec.org/a/eee/csdana/v57y2013i1p320-335.html
   My bibliography  Save this article

Sequential Monte Carlo for Bayesian sequentially designed experiments for discrete data

Author

Listed:
  • Drovandi, Christopher C.
  • McGree, James M.
  • Pettitt, Anthony N.

Abstract

In this paper we present a sequential Monte Carlo algorithm for Bayesian sequential experimental design applied to generalised non-linear models for discrete data. The approach is computationally convenient in that the information of newly observed data can be incorporated through a simple re-weighting step. We also consider a flexible parametric model for the stimulus–response relationship together with a newly developed hybrid design utility that can produce more robust estimates of the target stimulus in the presence of substantial model and parameter uncertainty. The algorithm is applied to hypothetical clinical trial or bioassay scenarios. In the discussion, potential generalisations of the algorithm are suggested to possibly extend its applicability to a wide variety of scenarios.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:csdana:v:57:y:2013:i:1:p:320-335
    DOI: 10.1016/j.csda.2012.05.014
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0167947312002137
    Download Restriction: Full text for ScienceDirect subscribers only.
    File URL: https://libkey.io/10.1016/j.csda.2012.05.014?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. 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.
    2. 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.
    3. Björn Bornkamp & Katja Ickstadt, 2009. "Bayesian Nonparametric Estimation of Continuous Monotone Functions with Applications to Dose–Response Analysis," Biometrics, The International Biometric Society, vol. 65(1), pages 198-205, March.
    4. Mauro Gasparini & Jeffrey Eisele, 2000. "A Curve-Free Method for Phase I Clinical Trials," Biometrics, The International Biometric Society, vol. 56(2), pages 609-615, June.
    5. N. Friel & A. N. Pettitt, 2008. "Marginal likelihood estimation via power posteriors," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 70(3), pages 589-607, July.
    6. Nadine Houede & Peter F. Thall & Hoang Nguyen & Xavier Paoletti & Andrew Kramar, 2010. "Utility-Based Optimization of Combination Therapy Using Ordinal Toxicity and Efficacy in Phase I/II Trials," Biometrics, The International Biometric Society, vol. 66(2), pages 532-540, June.
    7. Saurabh Mukhopadhyay, 2000. "Bayesian Nonparametric Inference on the Dose Level with Specified Response Rate," Biometrics, The International Biometric Society, vol. 56(1), pages 220-226, March.
    8. Stefanie Biedermann & David C. Woods, 2011. "Optimal designs for generalized non‐linear models with application to second‐harmonic generation experiments," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 60(2), pages 281-299, March.
    9. Nicolas Chopin, 2002. "A sequential particle filter method for static models," Biometrika, Biometrika Trust, vol. 89(3), pages 539-552, August.
    10. Guosheng Yin & Yisheng Li & Yuan Ji, 2006. "Bayesian Dose-Finding in Phase I/II Clinical Trials Using Toxicity and Efficacy Odds Ratios," Biometrics, The International Biometric Society, vol. 62(3), pages 777-787, September.
    11. Dror, Hovav A. & Steinberg, David M., 2008. "Sequential Experimental Designs for Generalized Linear Models," Journal of the American Statistical Association, American Statistical Association, vol. 103, pages 288-298, March.
    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. Ryan, Elizabeth G. & Drovandi, Christopher C. & Thompson, M. Helen & Pettitt, Anthony N., 2014. "Towards Bayesian experimental design for nonlinear models that require a large number of sampling times," Computational Statistics & Data Analysis, Elsevier, vol. 70(C), pages 45-60.
    2. Abebe, Haftom T. & Tan, Frans E.S. & Van Breukelen, Gerard J.P. & Berger, Martijn P.F., 2014. "Bayesian D-optimal designs for the two parameter logistic mixed effects model," Computational Statistics & Data Analysis, Elsevier, vol. 71(C), pages 1066-1076.
    3. Azriel, David, 2014. "Optimal sequential designs in phase I studies," Computational Statistics & Data Analysis, Elsevier, vol. 71(C), pages 288-297.
    4. 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.
    5. 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.
    6. Jacopo Paglia & Jo Eidsvik & Juha Karvanen, 2022. "Efficient spatial designs using Hausdorff distances and Bayesian optimization," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 49(3), pages 1060-1084, September.

    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. 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.
    2. Peter F. Thall & Hoang Q. Nguyen & Ralph G. Zinner, 2017. "Parametric dose standardization for optimizing two-agent combinations in a phase I–II trial with ordinal outcomes," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 66(1), pages 201-224, January.
    3. Ying Yuan & Guosheng Yin, 2009. "Bayesian dose finding by jointly modelling toxicity and efficacy as time‐to‐event outcomes," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 58(5), pages 719-736, December.
    4. Hai‐Dang Dau & Nicolas Chopin, 2022. "Waste‐free sequential Monte Carlo," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 84(1), pages 114-148, February.
    5. Mathias Drton & Martyn Plummer, 2017. "A Bayesian information criterion for singular models," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 79(2), pages 323-380, March.
    6. Drovandi, Christopher C. & Pettitt, Anthony N., 2011. "Likelihood-free Bayesian estimation of multivariate quantile distributions," Computational Statistics & Data Analysis, Elsevier, vol. 55(9), pages 2541-2556, September.
    7. Xing Ju Lee & Christopher C. Drovandi & Anthony N. Pettitt, 2015. "Model choice problems using approximate Bayesian computation with applications to pathogen transmission data sets," Biometrics, The International Biometric Society, vol. 71(1), pages 198-207, March.
    8. Arnaud Dufays, 2016. "Evolutionary Sequential Monte Carlo Samplers for Change-Point Models," Econometrics, MDPI, vol. 4(1), pages 1-33, March.
    9. Jeong Eun Lee & Christian Robert, 2013. "Imortance Sampling Schemes for Evidence Approximation in Mixture Models," Working Papers 2013-42, Center for Research in Economics and Statistics.
    10. 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.
    11. 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.
    12. 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.
    13. Ettmeier, Stephanie & Kriwoluzky, Alexander, 2019. "Active, or passive? Revisiting the role of fiscal policy in the Great Inflation," VfS Annual Conference 2019 (Leipzig): 30 Years after the Fall of the Berlin Wall - Democracy and Market Economy 203609, Verein für Socialpolitik / German Economic Association.
    14. 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.
    15. Stephanie Ettmeier & Alexander Kriwoluzky, 2020. "Active, or Passive? Revisiting the Role of Fiscal Policy in the Great Inflation," Discussion Papers of DIW Berlin 1872, DIW Berlin, German Institute for Economic Research.
    16. Li, Dan & Clements, Adam & Drovandi, Christopher, 2023. "A Bayesian approach for more reliable tail risk forecasts," Journal of Financial Stability, Elsevier, vol. 64(C).
    17. Kassandra Fronczyk & Athanasios Kottas, 2014. "A Bayesian approach to the analysis of quantal bioassay studies using nonparametric mixture models," Biometrics, The International Biometric Society, vol. 70(1), pages 95-102, March.
    18. Maxime Lenormand & Franck Jabot & Guillaume Deffuant, 2013. "Adaptive approximate Bayesian computation for complex models," Computational Statistics, Springer, vol. 28(6), pages 2777-2796, December.
    19. 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.
    20. Herbst, Edward & Schorfheide, Frank, 2019. "Tempered particle filtering," Journal of Econometrics, Elsevier, vol. 210(1), pages 26-44.

    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:57:y:2013:i:1:p:320-335. 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.