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

We consider the problem of computing optimal experimental designs with respect to a compound Bayes risk criterion, which includes various specific criteria, such as a linear criterion for prediction in a random coefficient regression model. We prove that this problem can be converted into a problem of constrained A-optimality in an artificial model, which allows us to directly use existing theoretical results and software tools. We demonstrate the application of the proposed method for the optimal design of a random coefficient regression model with respect to an integrated mean squared error criterion.