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Optimal Design of Dilution Experiments Under Volume Constraints

Journal article
Authors M. Zolghadr
Sergei Zuyev
Published in Journal of Agricultural Biological and Environmental Statistics
Volume 21
Issue 4
Pages 663-683
ISSN 1085-7117
Publication year 2016
Published at Department of Mathematical Sciences, Mathematical Statistics
Pages 663-683
Language en
Keywords Dilution experiment, Poisson parameter inference, Fisher information criteria, One-stage design, Design measure, Gradient methods, Variational analysis on measures, Stem cell counting, hematopoietic stem-cells, variational analysis, tangent sets, 2nd-order, placenta, models, space, Life Sciences & Biomedicine - Other Topics, Mathematical & Computational, Biology, Mathematics, hneider r, 1988, journal of microscopy-oxford, v151, p211, aloner k, 1989, journal of statistical planning and inference, v21, p191
Subject categories Mathematics


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.

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