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Sequential Monte Carlo for Bayesian sequentially designed experiments for discrete data

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  • 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
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    References listed on IDEAS

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    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.
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    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.
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    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. 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.
    4. 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.
    5. Azriel, David, 2014. "Optimal sequential designs in phase I studies," Computational Statistics & Data Analysis, Elsevier, vol. 71(C), pages 288-297.
    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.

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