Hierarchical Latin Hypercube Sampling

Vikram V. Garg and Roy H. Stogner

Journal of the American Statistical Association, 2017, vol. 112, issue 518, 673-682

Abstract: 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.

Date: 2017
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DOI: 10.1080/01621459.2016.1158717

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