Cluster Sampling For Morris Method Made Easy

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.