Bayesian optimal designs for multi-factor nonlinear models

This article is concerned with the Bayesian optimal design problem for multi-factor nonlinear models. In particular, the Bayesian psi q-optimality criterion proposed by Dette et al. (Stat Sinica 17:463-480, 2007) is considered. It is shown that the product-type designs are optimal for the additive multi-factor nonlinear models with or without constant term when the proposed sufficient conditions are satisfied. Some examples of application using the exponential growth models with several variables are presented to illustrate optimal designs based on the Bayesian psi q-optimality criterion considered.