Optimal designs can help experimenters obtain more accurate parameter estimates with reduced experimental time and cost. In this paper, we characterize the Expected Weighted (EW) D-optimal designs as robust designs against unknown parameter values for experiments under a general parametric model with discrete and continuous factors. When a pilot study is available, we recommend sample-based EW D-optimal designs for subsequent experiments. Otherwise, we recommend EW D-optimal designs under a prior distribution for model parameters. We propose an EW ForLion algorithm for finding EW D-optimal designs with mixed factors, and justify that the designs found by our algorithm are EW D-optimal. To facilitate potential users in practice, we also develop a rounding algorithm that converts an approximate design with mixed factors to exact designs with prespecified grid points and the total number of experimental units. By applying our algorithms for real experiments under multinomial logistic models or generalized linear models, we show that our designs are highly efficient with respect to locally D-optimal designs and more robust against parameter value misspecifications.

翻译：最优设计可帮助实验者在减少实验时间和成本的同时获得更精确的参数估计。本文在含离散与连续因素的通用参数模型下，将期望加权D最优设计刻画为对未知参数值具有鲁棒性的实验设计。当存在预实验数据时，我们推荐基于样本的期望加权D最优设计用于后续实验；反之，则推荐基于模型参数先验分布的期望加权D最优设计。我们提出用于求解混合因素期望加权D最优设计的EW ForLion算法，并证明该算法生成的设计满足期望加权D最优性。为方便实践应用，我们同时开发了将混合因素近似设计转化为预定义网格点与实验单元总数精确设计的舍入算法。通过将算法应用于多项逻辑模型或广义线性模型的真实实验，我们证明这些设计不仅相对于局部D最优设计具有高效性，且对参数值误设定具有更强的鲁棒性。