Computing optimal experimental designs with respect to a compound Bayes risk criterion

TL;DR

This paper introduces a novel approach to computing optimal experimental designs under a compound Bayes risk criterion by reformulating the problem as constrained A-optimality, enabling the use of advanced optimization algorithms.

Contribution

It presents a new method that transforms the design problem into a constrained A-optimality problem, allowing efficient computation using second-order cone programming techniques.

Findings

The method effectively computes optimal designs for random coefficient regression models.

It demonstrates the approach on an integrated mean squared error criterion.

The approach leverages recent optimization algorithms for improved efficiency.

Abstract

We consider the problem of computing optimal experimental design on a finite design space with respect to a compound Bayes risk criterion, which includes the linear criterion for prediction in a random coefficient regression model. We show that the problem can be restated as constrained A-optimality in an artificial model. This permits using recently developed computational tools, for instance the algorithms based on the second-order cone programming for optimal approximate design, and mixed-integer second-order cone programming for optimal exact designs. We demonstrate the use of the proposed method for the problem of computing optimal designs of a random coefficient regression model with respect to an integrated mean squared error criterion.