论文标题
D-和A-最佳筛选设计
D- and A-optimal Screening Designs
论文作者
论文摘要
在实践中，即使考虑[-1，1]中的级别的连续因子，即使考虑到连续因子，也使用固定在+/- 1的因子设置的D-Criterion来生成任意运行尺寸的最佳筛选设计。本文确定了此类D-最佳设计的不良估计方差属性的情况，并认为通常A-Aftimal设计倾向于将方差推向其最小值可能的最小值。有关标准行为的新见解是通过对各自坐标 - 交换公式的研究找到的。该研究证实了仅针对设置+/- 1组成的D-最佳设计的存在，用于阻塞和未阻止的实验的主要效果和相互作用模型。还确定了对[-1，1]之间对坐标的任意操纵的情况，导致无限许多具有不同方差属性的D-最佳设计。对于相同的条件，显示A标准具有唯一的最佳坐标值以进行改进。我们还比较了贝叶斯版的A-和D标准如何平衡估计方差和偏差的最小化。在贝叶斯和非乘坐版本的A型和D标准版本下，考虑了各种模型的筛选设计的多个示例。
In practice, optimal screening designs for arbitrary run sizes are traditionally generated using the D-criterion with factor settings fixed at +/- 1, even when considering continuous factors with levels in [-1, 1]. This paper identifies cases of undesirable estimation variance properties for such D-optimal designs and argues that generally A-optimal designs tend to push variances closer to their minimum possible value. New insights about the behavior of the criteria are found through a study of their respective coordinate-exchange formulas. The study confirms the existence of D-optimal designs comprised only of settings +/- 1 for both main effect and interaction models for blocked and un-blocked experiments. Scenarios are also identified for which arbitrary manipulation of a coordinate between [-1, 1] leads to infinitely many D-optimal designs each having different variance properties. For the same conditions, the A-criterion is shown to have a unique optimal coordinate value for improvement. We also compare Bayesian version of the A- and D-criteria in how they balance minimization of estimation variance and bias. Multiple examples of screening designs are considered for various models under Bayesian and non-Bayesian versions of the A- and D-criteria.
