Abstract Split-plot definitive screening and blocked definitive screening designs have been developed for detecting active main effects and second-order effects in screening experiments when split-plot and block structures exist. In the literature, multistage regression and forward stepwise regression methods were proposed for data analysis on the two types of designs. However, classical regression approaches present limitations and potential problems. First, the degrees of freedom may not be large enough to estimate all active effects. Second, the restricted maximum-likelihood estimates for variances of whole-plot and block errors can be zero. To solve these problems and enhance detection capability, we propose a stochastic search variable selection (SSVS) method based on Bayesian theory. Different from the existing Bayesian approaches for split-plot and blocked designs, the proposed SSVS method can perform variable selections and choose models that follow the effect heredity principle. Markov chain Monte Carlo and Gibbs sampling are applied and a general WinBUGS code, which can be used for any split-plot and blocked screening design, is provided. Simulation studies are conducted and their results show that the proposed SSVS method effectively controls the false discovery rate and has higher detection capability than the two regression methods.

中文翻译：

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裂区和分块筛选设计的随机搜索变量选择

摘要 裂区确定性筛选和分块确定性筛选设计已开发用于在存在裂区和块结构时检测筛选实验中的主动主效应和二阶效应。在文献中，提出了多阶段回归和正向逐步回归方法对两种设计进行数据分析。然而，经典回归方法存在局限性和潜在问题。首先，自由度可能不足以估计所有主动效应。其次，全区和块误差方差的受限最大似然估计可以为零。为了解决这些问题并增强检测能力，我们提出了一种基于贝叶斯理论的随机搜索变量选择（SSVS）方法。与现有的用于裂区和块设计的贝叶斯方法不同，所提出的 SSVS 方法可以执行变量选择并选择遵循效应遗传原则的模型。应用马尔可夫链蒙特卡罗和吉布斯采样，并提供了通用 WinBUGS 代码，可用于任何裂区和块筛选设计。仿真研究结果表明，所提出的SSVS方法有效地控制了错误发现率，并且比两种回归方法具有更高的检测能力。提供。仿真研究结果表明，所提出的SSVS方法有效地控制了错误发现率，并且比两种回归方法具有更高的检测能力。提供。仿真研究结果表明，所提出的SSVS方法有效地控制了错误发现率，并且比两种回归方法具有更高的检测能力。