A convex approach to optimum design of experiments with correlated observations

TL;DR

This paper introduces a convex optimization framework for designing experiments with correlated observations, providing a performance bound and a method for generating optimal designs, enhancing the evaluation of experimental strategies.

Contribution

It develops a convex formulation for optimal experimental design with correlated data, including an equivalence theorem, an upper bound algorithm, and a method for exact design generation.

Findings

The convex approach effectively evaluates design quality.

The algorithm provides a reliable upper performance bound.

Application to classical examples demonstrates practical utility.

Abstract

Optimal design of experiments for correlated processes is an increasingly relevant and active research topic. Present methods have restricted possibilities to judge their quality. To fill this gap, we complement the virtual noise approach by a convex formulation leading to an equivalence theorem comparable to the uncorrelated case and to an algorithm giving an upper performance bound against which alternative design methods can be judged. Moreover, a method for generating exact designs follows naturally. We exclusively consider estimation problems on a finite design space with a fixed number of elements. A comparison on some classical examples from the literature as well as a real application is provided.