Abstract
In the study of computer codes, filling space as uniformly as possible is important to describe the complexity of the investigated phenomenon. However, this property is not conserved by reducing the dimension. Some numeric experiment designs are conceived in this sense as Latin hypercubes or orthogonal arrays, but they consider only the projections onto the axes or the coordinate planes. We introduce a statistic which allows studying the good distribution of points according to all 1-dimensional projections. By angularly scanning the domain, we obtain a useful graphical representation. The advantages of this new tool are demonstrated on usual space-filling designs. Graphical, decisional and dimensionality issues are discussed.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Benjamini, Y. and Y. Hochberg (1995). Controlling the false discovery rate: a practical and powerful approach to multiple testing. Journal of the Royal Statistical Society, Series B 57, 289–300.
D’Agostino, R. and M. Stephens (1986). Goodness-of-fit Techniques. New York; Marcel Dekker.
Fang, K.-T., R. Li, and A. Sudjianto (2006). Design and Modeling for Computer Experiments. London: Chapman & Hall.
Fisher, R. A. (1926). The arrangement of field experiments. Journal of the Ministry of Agriculture 33, 503–513.
Fukumizu, K., F. Bach, and M. Jordan (2009). Kernel dimension reduction in regression. Annals of Statistics 37, 1871–1905.
Knuth, D. (1997). The Art of Computer Programming, Volume 2: Seminumerical Algorithms, 3rd edition. Reading MA: Addison-Wesley.
Koehler, J. and A. Owen (1996). Computer experiments. Amsterdam: Elsevier. Handbook of Statistics 13, 261–308.
L’Ecuyer, P. and R. Simard (2007). Testu01: A C library for empirical testing of random number generators. ACM Transactions on Mathematical Software 33(4), Article 22.
Li, K. (1991). Sliced inverse regression for dimension reduction (with discussion). Journal of the American Statistical Association 86, 316–342.
Loeppky, J., J. Sacks, and W. Welch (2008). Choosing the sample size of a computer experiment: A practical guide. Technical report, NISS.
Niederreiter, H. (1987). Low-discrepancy and low-dispersion sequences. Journal of Number Theory 30, 51–70.
Ripley, B. (1987). Stochastic Simulation. New York: Wiley.
Santner, T., B. Williams, and W. Notz (2003). The Design and Analysis of Computer Experiments. New York: Springer-Verlag.
Shiu, E. S. W. (1987). Convolution of uniform distributions and ruin probability. Scandinavian Actuarial Journal 70, 191–197.
Acknowledgements
We wish to thank A. Antoniadis, the members of the DICE Consortium (http://www.dice-consortium.fr), the participants of ENBIS-DEINDE 2007, as well as two referees for their useful comments. We also thank Chris Yukna for his help in editing.
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2010 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Roustant, O., Franco, J., Carraro, L., Jourdan, A. (2010). A Radial Scanning Statistic for Selecting Space-filling Designs in Computer Experiments. In: Giovagnoli, A., Atkinson, A., Torsney, B., May, C. (eds) mODa 9 – Advances in Model-Oriented Design and Analysis. Contributions to Statistics. Physica-Verlag HD. https://doi.org/10.1007/978-3-7908-2410-0_25
Download citation
DOI: https://doi.org/10.1007/978-3-7908-2410-0_25
Published:
Publisher Name: Physica-Verlag HD
Print ISBN: 978-3-7908-2409-4
Online ISBN: 978-3-7908-2410-0
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)