A PREDICTIVE APPROACH TO THE BAYESIAN DESIGN PROBLEM WITH APPLICATIONTO NORMAL REGRESSION-MODELS

A predictive decision-theoretic approach is developed for the Bayesian design problem. The loss functions used are fair Bayes, or proper sco ring rules, and are quadratic measures of distance between probability measures. Optimal Bayesian designs are those which minimise the prepo sterior risk for the decision problem. Such designs typically depend o n both the prior distribution and the loss function. The results are a pplied to certain normal regression models where explicit optimal desi gns are constructed.