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An induced natural selection heuristic for finding optimal Bayesian experimental designs

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  • Price, David J.
  • Bean, Nigel G.
  • Ross, Joshua V.
  • Tuke, Jonathan

Abstract

Bayesian optimal experimental design has immense potential to inform the collection of data so as to subsequently enhance our understanding of a variety of processes. However, a major impediment is the difficulty in evaluating optimal designs for problems with large, or high-dimensional, design spaces. An efficient search heuristic suitable for general optimisation problems, with a particular focus on optimal Bayesian experimental design problems, is proposed. The heuristic evaluates the objective (utility) function at an initial, randomly generated set of input values. At each generation of the algorithm, input values are “accepted” if their corresponding objective (utility) function satisfies some acceptance criteria, and new inputs are sampled about these accepted points. The new algorithm is demonstrated by evaluating the optimal Bayesian experimental designs for the previously considered death, pharmacokinetic and logistic regression models. Comparisons to the current “gold-standard” method are given to demonstrate the proposed algorithm as a computationally-efficient alternative for moderately-large design problems (i.e., up to approximately 40-dimensions).

Suggested Citation

  • 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.
    • Handle: RePEc:eee:csdana:v:126:y:2018:i:c:p:112-124
    DOI: 10.1016/j.csda.2018.04.011
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    References listed on IDEAS

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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.
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    4. 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.
    5. 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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