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Optimal Design of Dilution Experiments Under Volume Constraints

Author

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  • Maryam Zolghadr

    (University of Turin)

  • Sergei Zuyev

    (Chalmers University of Technology and University of Gothenburg)

Abstract

The paper develops methods to construct a one-stage optimal design of dilution experiments under the total available volume constraint typical for biomedical applications. We consider various design criteria based on the Fisher information both in Bayesian and non-Bayesian settings and show that the optimal design is typically one-atomic meaning that all the dilutions should be of the same size. The main tool is variational analysis of functions of a measure and the corresponding steepest descent-type numerical methods. Our approach is generic in the sense that it allows for inclusion of additional constraints and cost components, like the cost of materials and of the experiment itself.

Suggested Citation

  • Maryam Zolghadr & Sergei Zuyev, 2016. "Optimal Design of Dilution Experiments Under Volume Constraints," Journal of Agricultural, Biological and Environmental Statistics, Springer;The International Biometric Society;American Statistical Association, vol. 21(4), pages 663-683, December.
    • Handle: RePEc:spr:jagbes:v:21:y:2016:i:4:d:10.1007_s13253-016-0259-0
    DOI: 10.1007/s13253-016-0259-0
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    References listed on IDEAS

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    2. Holger Dette, 1997. "Designing Experiments with Respect to ‘Standardized’ Optimality Criteria," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 59(1), pages 97-110.
    3. Henry Wynn & Anatoly Zhigljavsky & Juan Romo, 1994. "The theory of search from a statistical viewpoint," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 3(2), pages 1-45, December.
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