Optimal Design of Dilution Experiments Under Volume Constraints

Maryam Zolghadr () and Sergei Zuyev ()
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Maryam Zolghadr: University of Turin
Sergei Zuyev: Chalmers University of Technology and University of Gothenburg

Journal of Agricultural, Biological and Environmental Statistics, 2016, vol. 21, issue 4, No 4, 663-683

Abstract: 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.

Keywords: Dilution experiment; Poisson parameter inference; Fisher information criteria; One-stage design; Design measure; Gradient methods; Variational analysis on measures; Stem cell counting; Primary 62K05; Secondary 62F15; 62F30; 65K10; 49K45 (search for similar items in EconPapers)
Date: 2016
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DOI: 10.1007/s13253-016-0259-0

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