Optimal and orthogonal Latin hypercube designs for computer experiments

Butler, Neil A.

doi:10.1093/biomet/88.3.847

Cited by 97 publications

(51 citation statements)

References 18 publications

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“…Table 1 OA(12, 2 10 , 2) and COD(12, 4 10 ) OA(12, 2 10 , 2) COD(12, 4 10 ) 6 , 2) and COD (18, 9 6 ) OA(18, 3 6 , 2) COD(18, 9 6 ) 1 1 …”

Section: Example 3 Supposementioning

confidence: 99%

Construction of column-orthogonal designs for computer experiments

Sun

2011

Sci. China Math.

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Latin hypercube design and uniform design are two kinds of most popular space-filling designs for computer experiments. The fact that the run size equals the number of factor levels in a Latin hypercube design makes it difficult to be orthogonal. While for a uniform design, it usually has good space-filling properties, but does not necessarily have small or zero correlations between factors. In this paper, we construct a class of column-orthogonal and nearly column-orthogonal designs for computer experiments by rotating groups of factors of orthogonal arrays, which supplement the designs for computer experiments in terms of various run sizes and numbers of factor levels and are flexible in accommodating various combinations of factors with different numbers of levels. The resulting column-orthogonal designs not only have uniformly spaced levels for each factor but also have uncorrelated estimates of the linear effects in first order models. Further, they are 3-orthogonal if the corresponding orthogonal arrays have strength equal to or greater than three. Along with a large factor-to-run ratio, these newly constructed designs are economical and suitable for screening factors for physical experiments.

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“…Table 1 OA(12, 2 10 , 2) and COD(12, 4 10 ) OA(12, 2 10 , 2) COD(12, 4 10 ) 6 , 2) and COD (18, 9 6 ) OA(18, 3 6 , 2) COD(18, 9 6 ) 1 1 …”

Section: Example 3 Supposementioning

confidence: 99%

Construction of column-orthogonal designs for computer experiments

Sun

2011

Sci. China Math.

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“…Designs based on (4) have previously been considered in the statistical design of experiments; see [2]. In that context, they are examples of Latin hypercube designs and the transformation from w (j ) to x (j ) is attributed to Williams [20].…”

Section: Integration Rulesmentioning

confidence: 99%

A new class of equal-weight integration rules on the hypercube

Butler

2004

Numer. Math.

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“…Even if the Latin Hypercube (LH) designs are not very satisfactory for space filling, they are satisfactory for space filling in individual directions, and this statement is valid for any number of design points. For a formal treatment of the subject see Welch et al (1992), Park (1994), Fang et al (2000), Butler (2001).…”

Section: Introductionmentioning

confidence: 99%