Optimal experimental design

Summary

Optimal experimental design chooses the conditions of an experiment so that the parameters of a given model are estimated as precisely as possible. Precision is measured by the information matrix of the design, and an optimality criterion turns that matrix into a number. D-optimality maximises its determinant, A-optimality minimises the trace of its inverse, and E-optimality maximises its smallest eigenvalue. The approximate theory, where a design is a probability measure on the design region, makes these problems convex. The Kiefer–Wolfowitz equivalence theorem shows that D-optimal and G-optimal designs coincide in that theory.