Bayesian experimental design for multiple hypothesis testing

The problem of designing an optimal experiment for the purpose of performing one or more hypothesis tests is Considered. The Bayesian decision theoretic approach is used to arrive at several new optimality criteria for this purpose. For a single hypothesis test, the resulting optimal designs are the well-known psi-optimal designs that minimize the posterior variance of the parameter being rested. For multiple tests, an experimental design must perform well under several competing criteria. Different approaches to achieving this goal are explored, including constrained optimization and an additive weighted loss. The resulting optimality criteria are sensitive not only to the posterior variances of the parameters under test but also to their prior means.