Nested Latin hypercube designs

• Published in: Biometrika Vol. 96; no. 4; pp. 957 - 970
• Main Author: QIAN, PETER Z. G.
• Format: Journal Article
• Language: English
• Published: Oxford Oxford University Press 01-12-2009; Biometrika Trust, University College London; Oxford University Press for Biometrika Trust; Oxford Publishing Limited (England)
• Series: Biometrika
• Subjects: Accuracy; Applications; Biology, psychology, social sciences; Combinatorics; Combinatorics. Ordered structures; Computer experiment; Computer modeling; Computers; Dams; Design; Design engineering; Design of experiment; Design optimization; Designs and configurations; Estimate reliability; Exact sciences and technology; Experiment design; Experimental design; General topics; Integers; Latin hypercube design; Linking parameter; Mathematics; Maximin; Multi-fidelity computer model; Probability and statistics; Probability mass distributions; Sciences and techniques of general use; Sequential evaluation; Space-filling design; Statistical methods; Statistics; Studies; Linking parameter; Computer experiment; Space-filling design; Multi-fidelity computer model; Design of experiment; Latin hypercube design; Sequential evaluation; Biometrics; Nested design; Implementation; Statistical method; Sequential method; Experimental design; Hypercube; Computing method
• ISSN: 0006-3444; 1464-3510; 1464-3510; 0006-3444
• DOI: 10.1093/biomet/asp045

We propose an approach to constructing nested Latin hypercube designs. Such designs are useful for conducting multiple computer experiments with different levels of accuracy. A nested Latin hypercube design with two layers is defined to be a special Latin hypercube design that contains a smaller Latin hypercube design as a subset. Our method is easy to implement and can accommodate any number of factors. We also extend this method to construct nested Latin hypercube designs with more than two layers. Illustrative examples are given. Some statistical properties of the constructed designs are derived.