DiceDesign (version 1.10)

DiceDesign-package: Designs of Computer Experiments

Description

Space-Filling Designs (SFD) and space-filling criteria (distance-based and uniformity-based).

Author

J. Franco, D. Dupuy, O. Roustant, P. Kiener, G. Damblin and B. Iooss. Thanks to A. Jourdan for discussions about OA131.

Maintainer: Celine Helbert

Details

This package provides tools to create some specific Space-Filling Design (SFD) and to test their quality:

• Latin Hypercube designs (randomized or centered)

• Strauss SFD and Maximum entropy SFD, WSP designs

• Optimal (low-discrepancy and maximin) Latin Hypercube desigsn by simulated annealing and genetic algorithms,

• Orthogonal and Nearly Orthogonal Latin Hypercube designs,

• Discrepancies criteria, distance measures,

• Minimal spanning tree criteria,

• Radial scanning statistic

References

Cioppa T.M., Lucas T.W. (2007). Efficient nearly orthogonal and space-filling Latin hypercubes. Technometrics 49, 45-55.

Damblin G., Couplet M., and Iooss B. (2013). Numerical studies of space filling designs: optimization of Latin Hypercube Samples and subprojection properties, Journal of Simulation, 7:276-289, 2013.

De Rainville F.-M., Gagne C., Teytaud O., Laurendeau D. (2012). Evolutionary optimization of low-discrepancy sequences. ACM Transactions on Modeling and Computer Simulation (TOMACS), 22(2), 9.

Dupuy D., Helbert C., Franco J. (2015), DiceDesign and DiceEval: Two R-Packages for Design and Analysis of Computer Experiments, Journal of Statistical Software, 65(11), 1--38.

Fang K.-T., Li R. and Sudjianto A. (2006) Design and Modeling for Computer Experiments, Chapman & Hall.

Fang K-T., Liu M-Q., Qin H. and Zhou Y-D. (2018) Theory and application of uniform experimental designs. Springer.

Nguyen N.K. (2008) A new class of orthogonal Latinhypercubes, Statistics and Applications, Volume 6, issues 1 and 2, pp.119-123.

Owen A.B. (2020), On dropping the first Sobol point, https://arxiv.org/abs/2008.08051.

Roustant O., Franco J., Carraro L., Jourdan A. (2010), A radial scanning statistic for selecting space-filling designs in computer experiments, MODA-9 proceedings.

Santner T.J., Williams B.J. and Notz W.I. (2003) The Design and Analysis of Computer Experiments, Springer, 121-161.

Examples

# **********************
# Designs of experiments
# **********************

# A maximum entropy design with 20 points in [0,1]^2
p <- dmaxDesign(20,2,0.9,200)
plot(p$design,xlim=c(0,1),ylim=c(0,1))

# Change the dimnames, adjust to range (-10, 10) and round to 2 digits
xDRDN(p, letter = "T", dgts = 2, range = c(-10, 10))

# ************************
# Criteria: L2-discrepancy
# ************************
dp <- discrepancyCriteria(p$design,type=c('L2','C2'))
# Coverage measure
covp <- coverage(p$design)

# *******************************
# Criteria: Minimal Spanning Tree
# *******************************
mstCriteria(p$design,plot2d=TRUE)

# ****************************************************************
# Radial scanning statistic: Detection of defects of Sobol designs
# ****************************************************************

# requires randtoolbox package
library(randtoolbox)

# in 2D
rss <- rss2d(design=sobol(n=20, dim=2), lower=c(0,0), upper=c(1,1),
	type="l", col="red")

# in 8D. All pairs of dimensions are tried to detect the worst defect
# (according to the specified goodness-of-fit statistic).
d <- 8
n <- 10*d
rss <- rss2d(design=sobol(n=n, dim=d), lower=rep(0,d), upper=rep(1,d),
	type="l", col="red")

# avoid this defect with scrambling ?
#    1. Faure-Tezuka scrambling (type "?sobol" for more details and options)
rss <- rss2d(design=sobol(n=n, dim=d, scrambling=2), lower=rep(0,d),
	upper=rep(1,d), type="l", col="red")
#    2. Owen scrambling
rss <- rss2d(design=sobol(n=n, dim=d, scrambling=1), lower=rep(0,d),
	upper=rep(1,d), type="l", col="red")