Weighted space-filling designs

Bowman, Veronica E; Woods, David C.

doi:10.1057/jos.2013.8

Cited by 16 publications

(17 citation statements)

References 30 publications

(25 reference statements)

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“…Performance was also strong for n = 42, with only x 3 and x 7 not identified. For both examples, relatively effective screening was achieved through use of a SFRD to estimate sensitivity indices (13). These estimated indices are displayed in Figure 5.…”

Section: Methods Using Gaussian Processes and Space-filling Designs: mentioning

confidence: 99%

“…Maximin LHS can be found using the R packages DiceDesign [40] and SLHD [5]. More general classes of distance-based space-filling designs, without the projection properties of the Latin hypercubes, can also be found [see 50,13]. Studies of the numerical efficiencies of optimization algorithms for LHS designs are available [49,29].…”

Section: Random Sampling Plans and Space-filling 41 Latin Hypercube mentioning

confidence: 99%

“…Objective function (16) arises from the use of a weighted Euclidean distance, see also [13]. Another important recent development is sliced LHS designs [89,88,6], where the design can be partitioned into sets of runs or slices, each of which is an orthogonal or maximin LHS.…”

Section: Random Sampling Plans and Space-filling 41 Latin Hypercube mentioning

confidence: 99%

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Design of Experiments for Screening

Woods

Lewis

2017

Handbook of Uncertainty Quantification

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The aim of this paper is to review methods of designing screening experiments, ranging from designs originally developed for physical experiments to those especially tailored to experiments on numerical models. The strengths and weaknesses of the various designs for screening variables in numerical models are discussed. First, classes of factorial designs for experiments to estimate main effects and interactions through a linear statistical model are described, specifically regular and nonregular fractional factorial designs, supersaturated designs and systematic fractional replicate designs. Generic issues of aliasing, bias and cancellation of factorial effects are discussed. Second, group screening experiments are considered including factorial group screening and sequential bifurcation. Third, random sampling plans are discussed including Latin hypercube sampling and sampling plans to estimate elementary effects. Fourth, a variety of modelling methods commonly employed with screening designs are briefly described. Finally, a novel study demonstrates six screening methods on two frequently-used exemplars, and their performances are compared.

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Section: Methods Using Gaussian Processes and Space-filling Designs: mentioning

confidence: 99%

Section: Random Sampling Plans and Space-filling 41 Latin Hypercube mentioning

confidence: 99%

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Design of Experiments for Screening

Woods

Lewis

2017

Handbook of Uncertainty Quantification

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“…Space-filling designs that account for statistical dependencies among the k inputs-which may be quantitative or qualitative-are given in Bowman and Woods (2013). A textbook is Lemieux (2009).…”

Section: Designs For Deterministic Simulationmentioning

confidence: 99%

Design and Analysis of Simulation Experiments

Kleijnen

2015

International Series in Operations Research &Amp; Management Science

194

138

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This chapter is organized as follows. Section 5.1 introduces Kriging, which is also called Gaussian process (GP) or spatial correlation modeling. Section 5.2 details so-called ordinary Kriging (OK), including the basic Kriging assumptions and formulas assuming deterministic simulation. Section 5.3 discusses parametric bootstrapping and conditional simulation for estimating the variance of the OK predictor. Section 5.4 discusses universal Kriging (UK) in deterministic simulation. Section 5.5 surveys designs for selecting the input combinations that gives input/output data to which Kriging metamodels can be fitted; this section focuses on Latin hypercube sampling (LHS) and customized sequential designs. Section 5.6 presents stochastic Kriging (SK) for random simulations. Section 5.7 discusses bootstrapping with acceptance/rejection for obtaining Kriging predictors that are monotonic functions of their inputs. Section 5.8 discusses sensitivity analysis of Kriging models through functional analysis of variance (FANOVA) using Sobol's indexes. Section 5.9 discusses risk analysis (RA) or uncertainty analysis (UA). Section 5.10 discusses several remaining issues. Section 5.11 summarizes the major conclusions of this chapter, and suggests topics for future research. The chapter ends with Solutions of exercises, and a long list of references.

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“…The technique relies on optimized permutations of an initial Latin hypercube design. Similarly, Bowman and Woods 66 proposed a method that optimizes space-filling designs, weighting the distance between points by multivariate dependencies between input variables. Saturated and supersaturated designs Comment: as discussed in the recent reviews, 67,68 there are cases, such as screening, where a relatively large number of input variables are studied.…”

Section: Constrained Design Spacementioning

confidence: 99%

A Tutorial on Latin Hypercube Design of Experiments

Viana

2015

Qual. Reliab. Engng. Int.

137

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The growing power of computers enabled techniques created for design and analysis of simulations to be applied to a large spectrum of problems and to reach high level of acceptance among practitioners. Generally, when simulations are time consuming, a surrogate model replaces the computer code in further studies (e.g., optimization, sensitivity analysis, etc.). The first step for a successful surrogate modeling and statistical analysis is the planning of the input configuration that is used to exercise the simulation code. Among the strategies devised for computer experiments, Latin hypercube designs have become particularly popular. This paper provides a tutorial on Latin hypercube design of experiments, highlighting potential reasons of its widespread use. The discussion starts with the early developments in optimization of the point selection and goes all the way to the pitfalls of the indiscriminate use of Latin hypercube designs. Final thoughts are given on opportunities for future research.

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Weighted space-filling designs

Cited by 16 publications

References 30 publications

Design of Experiments for Screening

Design of Experiments for Screening

Design and Analysis of Simulation Experiments

A Tutorial on Latin Hypercube Design of Experiments

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