Generating and validating cluster sampling matrices for model-free factor screening

Abstract

Morris’ elementary effect-based screening (MM) has been widely used in a variety of domains to identify a few important factors among many possible ones. In MM, cluster sampling offers substantial computational savings over non-cluster sampling, but it remains a challenge to construct a cluster sampling matrix that generates any particular number of elementary effects for each factor. In this paper, we thoroughly address this issue. We uncover the mathematical association between distinct block sampling matrices within the complete cluster sampling matrix, by introducing a “dummy” sub-block matrix. By leveraging this property, we propose an easy-to-implement adaptive cluster sampling (ACS) method that is capable of identifying the appropriate sub-block sampling matrix to use. Its advantage over existing brute-force methods is that it can provide easy-to-obtain cluster sampling matrices, and it can be applied to computational model with any number of factors given a prior. We demonstrate the attractive properties of ACS using analytical proofs and simulation experiments. We show the robustness of ACS via a real-world case study. Our code for the algorithm is available online.