Optimal Sliced Latin Hypercube Designs

Ba, Shan; Myers, William; Brenneman, William A.

doi:10.1080/00401706.2014.957867

Cited by 137 publications

(81 citation statements)

References 14 publications

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“…By choosing different A, B, and C q 's, the proposed methods produce a vast class of Latin hypercubes. We show empirically that this class contains designs whose maximin criterion values can be comparable to those produced by the R packages lhs (Carnell (2012)) and SLHD (Ba (2013) ;Ba, Brenneman, and Myers (2014)). The first package has been used frequently in practice and in the literature and the latter is relatively new and has been shown to perform better than some existing ones.…”

Section: Applicationsmentioning

confidence: 98%

A general construction for space-filling Latin hypercubes

Lin¹,

Kang²

2017

STAT SINICA

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We propose a general method for constructing Latin hypercubes of flexible run sizes for computer experiments. The method makes use of arrays with a special structure and Latin hypercubes. By using different such arrays and Latin hypercubes, the proposed method produces various types of Latin hypercubes including orthogonal and nearly orthogonal Latin hypercubes, sliced Latin hypercubes, and Latin hypercubes in marginally coupled designs. In addition, the proposed algebraic design construction is particularly efficient as it does not need any optimization search but still produces Latin hypercubes whose space-filling properties are comparable with those generated by the common and latest methods in the literature.

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Section: Applicationsmentioning

confidence: 98%

A general construction for space-filling Latin hypercubes

Lin¹,

Kang²

2017

STAT SINICA

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“…Expert judgement is also needed to define the ranges of these inputs. A space-filling design such as maximin Latin hypercube sampling or sliced Latin hypercube sampling (Ba et al, 2015) is required in order to sample from the input space with the minimum sufficient number of model runs. We used n = 10 000 for the Sobol method and n = 5000 for the eFAST method, but n = N = 80 for the GAM and PLS methods.…”

Section: Methodsmentioning

confidence: 99%

Fast sensitivity analysis methods for computationally expensive models with multi-dimensional output

et al. 2018

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Abstract. Global sensitivity analysis (GSA) is a powerful approach in identifying which inputs or parameters most affect a model's output. This determines which inputs to include when performing model calibration or uncertainty analysis. GSA allows quantification of the sensitivity index (SI) of a particular input -the percentage of the total variability in the output attributed to the changes in that input -by averaging over the other inputs rather than fixing them at specific values. Traditional methods of computing the SIs using the Sobol and extended Fourier Amplitude Sensitivity Test (eFAST) methods involve running a model thousands of times, but this may not be feasible for computationally expensive Earth system models. GSA methods that use a statistical emulator in place of the expensive model are popular, as they require far fewer model runs. We performed an eight-input GSA, using the Sobol and eFAST methods, on two computationally expensive atmospheric chemical transport models using emulators that were trained with 80 runs of the models. We considered two methods to further reduce the computational cost of GSA: (1) a dimension reduction approach and (2) an emulator-free approach. When the output of a model is multi-dimensional, it is common practice to build a separate emulator for each dimension of the output space. Here, we used principal component analysis (PCA) to reduce the output dimension, built an emulator for each of the transformed outputs, and then computed SIs of the reconstructed output using the Sobol method. We considered the global distribution of the annual column mean lifetime of atmospheric methane, which requires ∼ 2000 emulators without PCA but only 5-40 emulators with PCA. We also applied an emulator-free method using a generalised additive model (GAM) to estimate the SIs using only the training runs. Compared to the emulator-only methods, the emulator-PCA and GAM methods accurately estimated the SIs of the ∼ 2000 methane lifetime outputs but were on average 24 and 37 times faster, respectively.

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“…Nested Latin hypercube designs are popular researched in recently years [[3], [4], [5]], which mostly deal with the high-accuracy and low-accuracy experiments, where Sliced Latin hypercube designs are similar to the Nested one[ [10], [11], [12]]. Meanwhile, a new method to construct SLHD is proposed in [9]. But in some special situations, e.g., the captive flight tests and missile tests in radar homing precision experiments, the ranges of factors are different in the original experiment and substitution experiment, NLHD could not deal with this situations and the existing methods deal almost exclusively with experiments which have same ranges of factors.…”

Section: Introductionmentioning

confidence: 99%

A New Nested Space-Filling Designs on Experiments With Different Ranges of Factors

Xu¹,

Duan²,

Wang³

et al. 2017

Proceedings of the 2nd International Conference on Uncertainty Quantification in Computational Sciences and Engineering (UNCECO

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Abstract. Experiments with different levels of accuracy or fidelity are very common in statistics, applied mathematics and engineering. Nested space-filling designs are useful approach to deal with those questions. But in some special situations, e.g., the captive flight tests and missile tests in radar homing precision experiments, the rangers of factors are different in some accuracy experiments and sometimes they have overlapping portions. The existing methods deal almost exclusively with experiments with same ranges of factors. In this paper, we propose a new construction of nested space-filling designs named NDF(Nested Designs on Factor with different ranges ) to solve these problems.The proposed construction are useful in the experiments with different ranges of factors and achieves uniformity in low dimensions.

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Optimal Sliced Latin Hypercube Designs

Cited by 137 publications

References 14 publications

A general construction for space-filling Latin hypercubes

A general construction for space-filling Latin hypercubes

Fast sensitivity analysis methods for computationally expensive models with multi-dimensional output

A New Nested Space-Filling Designs on Experiments With Different Ranges of Factors

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