An Efficient Bayesian Optimal Design for Logistic Model

Consider a Bayesian optimal design with many support points which poses the problem of collecting data with a few number of observations at each design point. Under such a scenario the asymptotic property of using Fisher information matrix for approximating the covariance matrix of posterior ML estimators might be doubtful. We suggest to use Bhattcharyya matrix in deriving the information matrix, led to modified Bayesian D-optimal criterion. This criterion is used to obtain optimal design for logistic model. It is shown that the resulting optimal design is more efficient than design given by Chaloner and Larentz (1989) using ordinary Bayesian D-optimal criterion.