Fractional polynomial models are potentially useful for response surfaces investigations. With the availability of routines for fitting nonlinear models in statistical packages they are increasingly being used. However, as in all experiments the design should be chosen such that the model parameters are estimated as efficiently as possible. The design choice for such models involves the known nonlinear models' design difficulties but \cite{gilmour_trinca_2012b} proposed a methodology capable of producing exact designs that makes use of the computing facilities available today. In this paper, we use this methodology to find Bayesian optimal exact designs for several fractional polynomial models. The optimum designs are compared to various standard designs in response surface problems.

翻译：分数多项式模型在响应曲面研究中具有潜在应用价值。随着统计软件包中非线性模型拟合程序的普及，这类模型正得到日益广泛的应用。然而，与所有实验设计一样，需要选择能使模型参数估计效率最大化的设计方案。此类模型的设计选择涉及经典非线性模型的设计难题，但Gilmour与Trinca（2012b）提出了一种能够利用现代计算设施生成精确设计方案的方法论。本文运用该方法论为若干分数多项式模型寻找贝叶斯最优精确设计，并将所得最优设计与响应曲面问题中的多种标准设计进行比较。