Bayesian Φq-optimal designs for multi-factor additive non linear models with heteroscedastic errors

This article considers Bayesian phi(q)-optimal designs for multi-factor additive non linear models where model errors are heteroscedastic. For additive non linear models with a constant term, a sufficient condition is given in order to derive Bayesian phi(q)-optimal product designs, which are achieved from univariate optimal designs with respect to every marginal model with a single factor. However, in the case of ignoring a constant term, an additional assumption of orthogonality is proposed to ensure that optimal designs can be found. Then, the corresponding optimal product designs can be built with the help of the equivalence theorem for the Bayesian phi(q)-optimality criterion. Several examples are given to illustrate the effectiveness of theoretical results on optimal product designs.