Construction of sliced maximin-orthogonal Latin hypercube designs

Yang, Jinyu; Chen, Hao; Lin, Dennis K.J.; Liu, Min Qian

doi:10.5705/ss.2013.352

Cited by 11 publications

(15 citation statements)

References 22 publications

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“…Yang, Lin, Qian, and Lin ; Huang, Yang, and Liu ; and Cao and Liu mainly constructed orthogonal and nearly orthogonal SLHDs, but orthogonality does not guarantee a good uniformity. Yang, Chen, Lin, and Liu generated orthogonal SLHDs and improved their overall space‐filling property under the maximin distance criterion, but the uniformity of the slices was not considered. Yin, Lin, and Liu only focused on low‐dimensional projective stratification, and Yang, Chen, and Liu only considered the uniformity of the whole SLHDs.…”

Section: Concluding Remarks and Discussionmentioning

confidence: 99%

“…An n × q matrix S is called an SLHD with s slices, denoted by SL(n, q, s), if S is an L(n, q) and can be partitioned into s slices each of which is an L(m, q) with m = n∕s after the n levels are collapsed to m equally spaced levels according to ⌈i∕s⌉ for level i, where ⌈a⌉ means the smallest integer greater than or equal to a. SLHDs inherit the good property of LHDs, that is, they possess maximum stratification in any one dimension as well as their slices. Further studies on SLHDs include some constructions ensuring good projection in more than one dimension or orthogonality between columns, that is, Yang, Lin, Qian, and Lin [5]; Huang, Yang, and Liu [6]; Cao and Liu [7]; and Yang, Chen, Lin, and Liu [8] proposed methods to construct orthogonal and nearly orthogonal SLHDs. Yin, Lin, and Liu [9] constructed SLHDs with an attractive low-dimensional stratification via orthogonal arrays, and Yang, Chen, and Liu [10] obtained SLHDs based on resolvable orthogonal arrays.…”

Section: Introductionmentioning

confidence: 99%

“…SLHDs inherit the good property of LHDs, that is, they possess maximum stratification in any one dimension as well as their slices. Further studies on SLHDs include some constructions ensuring good projection in more than one dimension or orthogonality between columns, that is, Yang, Lin, Qian, and Lin ; Huang, Yang, and Liu ; Cao and Liu ; and Yang, Chen, Lin, and Liu proposed methods to construct orthogonal and nearly orthogonal SLHDs. Yin, Lin, and Liu constructed SLHDs with an attractive low‐dimensional stratification via orthogonal arrays, and Yang, Chen, and Liu obtained SLHDs based on resolvable orthogonal arrays.…”

Section: Introductionmentioning

confidence: 99%

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Uniform sliced Latin hypercube designs

Chen

Huang

Lin

et al. 2016

Appl Stoch Models Bus & Ind

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Sliced Latin hypercube designs (SLHDs) achieve maximum stratification in each dimension, but neither the full designs nor their slices can guarantee a good uniformity over the experimental region. Although the uniformity of the full SLHD and that of its slices are related, there is no one-to-one correspondence between them. In this paper, we propose a new uniformity measure for SLHDs by combining the two kinds of uniformity. Based on such a combined uniformity measure, the obtained uniform SLHDs have the design points evenly spread over the experimental region not only for the whole designs but also for their slices. Numerical simulation shows the effectiveness of the proposed uniform SLHDs for computer experiments with both quantitative and qualitative factors.

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Section: Concluding Remarks and Discussionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Uniform sliced Latin hypercube designs

Chen

Huang

Lin

et al. 2016

Appl Stoch Models Bus & Ind

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“…A design is said to be orthogonal if the correlation between any two distinct columns is zero. An SL(n, q, s) is called a sliced orthogonal LHD (SOLHD, [7][8][9][10][11][12]), denoted by SOL(n, q, s), if both the whole design and its slices are orthogonal. From the construction method in Algorithm 2.1, if the original SLHD in Step 2 is an SOLHD, then the obtained IBLHD will inherit the orthogonality to some extent.…”

Section: Nearly Orthogonal Iblhdsmentioning

confidence: 99%

“…From the construction method in Algorithm 2.1, if the original SLHD in Step 2 is an SOLHD, then the obtained IBLHD will inherit the orthogonality to some extent. In this paper, we only take the SOLHDs constructed by Algorithm 1 in [10] as the SLHDs in Step 2 of Algorithm 2.1. Other SOLHDs in the aforementioned literature can also be used of course, and the results will be similar, that is, the resulting IBLHDs are nearly orthogonal.…”

Section: Nearly Orthogonal Iblhdsmentioning

confidence: 99%

Construction of Improved Branching Latin Hypercube Designs

2021

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In this paper, we propose a new method, called the level-collapsing method, to construct branching Latin hypercube designs (BLHDs). The obtained design has a sliced structure in the third part, that is, the part for the shared factors, which is desirable for the qualitative branching factors. The construction method is easy to implement, and (near) orthogonality can be achieved in the obtained BLHDs. A simulation example is provided to illustrate the effectiveness of the new designs.

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A method of constructing optimal sliced uniform designs under discrete discrepancy

Yin

Huang

2021

Stat

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Sliced uniform designs are useful for generating experimental data with batch structures. In this paper, we employ the discrete discrepancy as the measure of uniformity to construct sliced uniform designs. The construction method is based on an important class of combinatorial configurations, namely, resolvable balanced incomplete block designs; hence, the construction method does not require any computer search. Through resolvable balanced incomplete block designs, under the discrete discrepancy, several infinite classes of new sliced uniform designs are obtained. The obtained design is optimal in the sense that not only the design as a whole but also each of its slices attain the lower bound of the discrete discrepancy. The design parameters are explicitly given, from which experimenters may choose an optimal sliced uniform design with the most suitable run size for their experiment. K E Y W O R D S design of experiments, incomplete block design, resolvability, uniformity, ∖special t4ht@. U-type design 1 | INTRODUCTION Sliced space-filling designs is a class of contemporary experimental designs which are useful for computer experiments with qualitative and quantitative factors, multilevel function estimation, stochastic optimization, cross-validation, and data pooling (

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Construction of sliced maximin-orthogonal Latin hypercube designs

Cited by 11 publications

References 22 publications

Uniform sliced Latin hypercube designs

Uniform sliced Latin hypercube designs

Construction of Improved Branching Latin Hypercube Designs

A method of constructing optimal sliced uniform designs under discrete discrepancy

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