×

Designing a computer experiment that involves switches. (English) Zbl 05902634

Summary: The use of Gaussian process emulators is now widespread in the analysis of computer experiments. These methods generally assume that all the simulator inputs are continuous. In this paper we consider the design problem for the case where one or more simulator inputs is a switch, a factor that can take the values on or off. We propose two possible designs: one based on Sobol sequences and one on Latin Hypercubes. In both cases a small, but space filling, subset of simulator runs are carried out at both switch settings. This design is then nested within larger space filling designs one for each of the switch settings. If the switch is found to not affect the results these two designs can be combined into a much larger also space filling design.

MSC:

62-XX Statistics

Software:

R; TOMS659
PDFBibTeX XMLCite
Full Text: DOI

References:

[1] Bratley, P.; Fox, B., ALGORITHM 659: implementing Sobol’s quasirandom sequence generator, ACM Transactions on Mathematical Software (TOMS), 14, 88-100 (1988) · Zbl 0642.65003 · doi:10.1145/42288.214372
[2] Halton, J., On the efficiency of certain quasi-random sequences of points in evaluating multidimensional integrals, Numerische Mathematik, 2, 84-90 (1960) · Zbl 0090.34505 · doi:10.1007/BF01386213
[3] Han, G.; Santner, TJ; Notz, WI; Bartel, DL, Prediction for computer experiments having quantitative and qualitative input variables, Technometrics, 513, 278-288 (2009) · doi:10.1198/tech.2009.07132
[4] Johnson, M.; Moore, L.; Ylvisaker, D., Minimax and maximin distance designs, Journal of Statistical Planning and Inference, 26, 131-148 (1990) · doi:10.1016/0378-3758(90)90122-B
[5] Joseph, VR; Hung, Y., Orthogonal-maximin Latin Hypercube designs, Stat Sinica, 18, 171-186 (2008) · Zbl 1137.62050
[6] Kennedy, M.; O’Hagan, A., Predicting the output from a complex computer code when fast approximations are available, Biometrika, 87, 1-13 (2000) · Zbl 0974.62024 · doi:10.1093/biomet/87.1.1
[7] Loeppky, JL; Sacks, J.; Welch, WJ, Choosing the sample size of a computer experiment: A practical guide, Technometrics, 51, 366-376 (2009) · doi:10.1198/TECH.2009.08040
[8] Maruri-Aguilar, H., 2010. Personal communication.
[9] McKay, M.; Beckman, R.; Conover, W., A comparison of three methods for selecting values of input variables in the analysis of output from a computer code, Technometrics, 21, 239-245 (1979) · Zbl 0415.62011
[10] Niederreiter, H., Random number generation and quasi-Monte Carlo methods (1992), Philadelphia. · Zbl 0761.65002
[11] O’Hagan, Bayesian analysis of computer code output: A tutorial, Reliability Engineering and System Safety, 91, 1290-1300 (2006) · doi:10.1016/j.ress.2005.11.025
[12] Owen, A., Orthogonal arrays for computer experiments, integration and visualization, Stat Sinica, 2, 439-452 (1992) · Zbl 0822.62064
[13] Qian, PZG, Nested Latin Hypercube designs, Biometrika, 96, 957-970 (2009) · Zbl 1179.62103 · doi:10.1093/biomet/asp045
[14] Qian, PZG; Wu, CFJ, Sliced space-filling designs, Biometrika, 96, 945-956 (2009) · Zbl 1179.62104 · doi:10.1093/biomet/asp044
[15] Qian, PZG; Wu, H.; Wu, CFJ, Gaussian process models for computer experiments with qualitative and quantitative factors, Technometrics, 50, 383-396 (2008) · doi:10.1198/004017008000000262
[16] R Development Core Team, 2010. R: A Language and Environment for Statistical Computing. R Foundation for Statistical Computing, Vienna, Austria.
[17] Santner, T.J., Williams, B.J., Notz, W.I., 2003. The design and analysis of computer experiments. Springer Verlag, New York. · Zbl 1041.62068 · doi:10.1007/978-1-4757-3799-8
[18] Sobol, L., On the distribution of points in a cube and the approximate evaluation of on the distribution of points in a cube and the approximate evaluation of integrals, USSR Comput. Math. and Math. Phys., 7, 86-112 (1967) · Zbl 0185.41103 · doi:10.1016/0041-5553(67)90144-9
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.