Nested Maximin Latin Hypercube Designs

CentER Discussion Paper Series No. 2009-06

21 Pages Posted: 19 Jan 2009

See all articles by Gijs Rennen

Gijs Rennen

Tilburg University - Department of Econometrics & Operations Research

Bart Husslage

Tilburg University - Department of Econometrics & Operations Research

Edwin van Dam

Tilburg University - Department of Econometrics & Operations Research

Dick den Hertog

Tilburg University - Department of Econometrics & Operations Research

Date Written: January 16, 2009

Abstract

In the field of design of computer experiments (DoCE), Latin hypercube designs are frequently used for the approximation and optimization of black-boxes. In certain situations, we need a special type of designs consisting of two separate designs, one being a subset of the other. These nested designs can be used to deal with training and test sets, models with different levels of accuracy, linking parameters, and sequential evaluations. In this paper, we construct nested maximin Latin hypercube designs for up to ten dimensions. We show that different types of grids should be considered when constructing nested designs and discuss how to determine which grid to use for a specific application.

To determine nested maximin designs for dimensions higher than two, four different variants of the ESE-algorithm of Jin et al. (2005) are introduced and compared. In the appendix, maximin distances for different numbers of points are provided.

Keywords: Design of computer experiments, Latin hypercube design, linking parameter, nested designs, sequential simulation, space-filling, training and test set

JEL Classification: C90

Suggested Citation

Rennen, Gijs and Husslage, Bart and van Dam, Edwin and den Hertog, Dick, Nested Maximin Latin Hypercube Designs (January 16, 2009). CentER Discussion Paper Series No. 2009-06. Available at SSRN: https://ssrn.com/abstract=1329897 or http://dx.doi.org/10.2139/ssrn.1329897

Gijs Rennen (Contact Author)

Tilburg University - Department of Econometrics & Operations Research ( email )

Tilburg, 5000 LE
Netherlands

Bart Husslage

Tilburg University - Department of Econometrics & Operations Research ( email )

Tilburg, 5000 LE
Netherlands

Edwin Van Dam

Tilburg University - Department of Econometrics & Operations Research ( email )

Tilburg, 5000 LE
Netherlands

Dick Den Hertog

Tilburg University - Department of Econometrics & Operations Research ( email )

Tilburg, 5000 LE
Netherlands

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