Bayesian A-Optimal Design of Experiment with Quantitative and Qualitative Responses

We consider the problem of A-optimal design of experiment under a Bayesian probabilistic model with both categorical and continuous response variables. The utility function of the local design problem is derived by applying Bayesian experimental design framework. We also develop an efficient optimization algorithm to obtain the local optimal design by combining the particle swarm optimization and the blocked coordinate descent methods. In addition, we discuss two different ways of constructing the global optimal design based on the algorithm for local optimal design. Simulation studies are presented to illustrate the efficiency of our approach.