This article is concerned with the Bayesian optimal design problem for multi-factor nonlinear models. In particular, the Bayesian \(\varPsi _q\)-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 \(\varPsi _q\)-optimality criterion considered.

中文翻译：

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多因素非线性模型的贝叶斯最优设计

本文涉及多因素非线性模型的贝叶斯最优设计问题。特别是，由Dette等人提出的贝叶斯\（\ varPsi _q \）-最优性准则。（Stat Sinica 17：463–480，2007）被考虑。结果表明，当满足建议的充分条件时，乘积型设计对于具有或不具有常数项的加性多因素非线性模型都是最佳的。给出了使用具有几个变量的指数增长模型的一些应用示例，以说明基于考虑的贝叶斯\（\ varPsi _q \）-最优性准则的最优设计。