Hierarchical Latin Hypercube Sampling
提出一种生成可递归划分为拉丁超立方子集的分层拉丁超立方集算法，并基于此开发分层增量拉丁超立方方法，允许用户灵活增量采样，克服了传统方法需预先选定全部样本或增量过大的缺点。
Latin hypercube sampling (LHS) is a robust, scalable Monte Carlo method that is used in many areas of science and engineering. We present a new algorithm for generating hierarchic Latin hypercube sets (HLHS) that are recursively divisible into LHS subsets. Based on this new construction, we introduce a hierarchical incremental LHS (HILHS) method that allows the user to employ LHS in a flexibly incremental setting. This overcomes a drawback of many LHS schemes that require the entire sample set to be selected a priori, or only allow very large increments. We derive the sampling properties for HLHS designs and HILHS estimators. We also present numerical studies that showcase the flexible incrementation offered by HILHS.