In this paper we provide a thorough investigation of the cluster sampling scheme for Morris' elementary effects method (MM), a popular model‐free factor screening method originated in the setting of design and analysis of computational experiments. We first study the sampling mechanism underpinning the two sampling schemes of MM (i.e., cluster sampling and noncluster sampling) and unveil its nature as a two‐level nested sampling process. This in‐depth understanding sets up a foundation for tackling two important aspects of cluster sampling: budget allocation and sampling plan. On the one hand, we study the budget allocation problem for cluster sampling under the analysis of variance framework and derive optimal budget allocations for efficient estimation of the importance measures. On the other hand, we devise an efficient cluster sampling algorithm with two variants to achieve enhanced statistical properties. The numerical evaluations demonstrate the superiority of the proposed cluster sampling algorithm and the budget allocations derived (when used both separately and in conjunction) to existing cluster and noncluster sampling schemes.

中文翻译：

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莫里斯方法的整群抽样变得容易

在本文中，我们对Morris基本效应方法（MM）的聚类采样方案进行了深入研究，该方法是一种流行的无模型因子筛选方法，起源于设计和计算实验分析的设置。我们首先研究了支持MM的两种采样方案（即集群采样和非集群采样）的采样机制，并揭示了其作为两级嵌套采样过程的本质。这种深入的了解为解决群集抽样的两个重要方面奠定了基础：预算分配和抽样计划。一方面，我们在方差分析的框架下研究了聚类抽样的预算分配问题，并得出了用于有效评估重要指标的最优预算分配。另一方面，我们设计了一种高效的群集采样算法，该算法具有两个变体，以实现增强的统计特性。数值评估证明了所提出的集群采样算法的优越性以及将预算分配（当单独使用和结合使用时）相对于现有集群和非集群采样方案的优越性。