Optimal design of dilution experiments under volume constraints

TL;DR

This paper presents a method for designing optimal dilution experiments under volume constraints, using variational analysis and Fisher information criteria, applicable in biomedical research.

Contribution

It introduces a generic variational approach for optimal design of dilution experiments, accommodating various constraints and cost factors.

Findings

Optimal designs are typically one-atomic, with all dilutions of the same size.

The approach uses variational analysis and steepest descent methods.

Method is flexible for additional constraints and cost considerations.

Abstract

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.