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Towards Bayesian experimental design for nonlinear models that require a large number of sampling times

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  • Ryan, Elizabeth G.
  • Drovandi, Christopher C.
  • Thompson, M. Helen
  • Pettitt, Anthony N.

Abstract

The use of Bayesian methodologies for solving optimal experimental design problems has increased. Many of these methods have been found to be computationally intensive for design problems that require a large number of design points. A simulation-based approach that can be used to solve optimal design problems in which one is interested in finding a large number of (near) optimal design points for a small number of design variables is presented. The approach involves the use of lower dimensional parameterisations that consist of a few design variables, which generate multiple design points. Using this approach, one simply has to search over a few design variables, rather than searching over a large number of optimal design points, thus providing substantial computational savings. The methodologies are demonstrated on four applications, including the selection of sampling times for pharmacokinetic and heat transfer studies, and involve nonlinear models. Several Bayesian design criteria are also compared and contrasted, as well as several different lower dimensional parameterisation schemes for generating the many design points.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:csdana:v:70:y:2014:i:c:p:45-60
    DOI: 10.1016/j.csda.2013.08.017
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    References listed on IDEAS

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    1. 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.
    2. Peter Müller & Don A. Berry & Andrew P. Grieve & Michael Krams, 2006. "A Bayesian Decision-Theoretic Dose-Finding Trial," Decision Analysis, INFORMS, vol. 3(4), pages 197-207, December.
    3. Concha Bielza & Peter Müller & David Ríos Insua, 1999. "Decision Analysis by Augmented Probability Simulation," Management Science, INFORMS, vol. 45(7), pages 995-1007, July.
    4. Alex R. Cook & Gavin J. Gibson & Christopher A. Gilligan, 2008. "Optimal Observation Times in Experimental Epidemic Processes," Biometrics, The International Biometric Society, vol. 64(3), pages 860-868, September.
    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. Jonathan R. Stroud & Peter Müller & Gary L. Rosner, 2001. "Optimal sampling times in population pharmacokinetic studies," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 50(3), pages 345-359.
    7. Christopher C. Drovandi & Anthony N. Pettitt, 2013. "Bayesian Experimental Design for Models with Intractable Likelihoods," Biometrics, The International Biometric Society, vol. 69(4), pages 937-948, December.
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    Cited by:

    1. Ryan, Elizabeth G. & Drovandi, Christopher C. & Pettitt, Anthony N., 2015. "Simulation-based fully Bayesian experimental design for mixed effects models," Computational Statistics & Data Analysis, Elsevier, vol. 92(C), pages 26-39.
    2. Price, David J. & Bean, Nigel G. & Ross, Joshua V. & Tuke, Jonathan, 2018. "An induced natural selection heuristic for finding optimal Bayesian experimental designs," Computational Statistics & Data Analysis, Elsevier, vol. 126(C), pages 112-124.
    3. Dehideniya, Mahasen B. & Drovandi, Christopher C. & McGree, James M., 2018. "Optimal Bayesian design for discriminating between models with intractable likelihoods in epidemiology," Computational Statistics & Data Analysis, Elsevier, vol. 124(C), pages 277-297.
    4. Elizabeth G. Ryan & Christopher C. Drovandi & James M. McGree & Anthony N. Pettitt, 2016. "A Review of Modern Computational Algorithms for Bayesian Optimal Design," International Statistical Review, International Statistical Institute, vol. 84(1), pages 128-154, April.

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