Optimal design of dilution experiments under volume constraints

The paper develops methods to construct a one-stage optimal design of dilution experiments under the total available volume constraint typical for bio-medical applications. We consider various design criteria based on the Fisher information both is Bayesian and non-Bayasian 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.