Journal of Statistical Theory and Practice

, Volume 5, Issue 1, pp 47–57

# Designing a Computer Experiment that Involves Switches

Article

## Abstract

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.

## Key-words

Computer experiments Switches Sobol sequence Latin hypercube

05B15

## References

1. Bratley, P., Fox, B., 1988. ALGORITHM 659: implementing Sobol’s quasirandom sequence generator. ACM Transactions on Mathematical Software (TOMS), 14(1), 88–100.
2. Halton, J., 1960. On the efficiency of certain quasi-random sequences of points in evaluating multidimensional integrals. Numerische Mathematik, 2, 84–90.
3. Han, G., Santner, T.J., Notz, W.I., Bartel, D.L., 2009. Prediction for computer experiments having quantitative and qualitative input variables. Technometrics, 51(3), 278–288.
4. Johnson, M., Moore, L., Ylvisaker, D., 1990. Minimax and maximin distance designs. Journal of Statistical Planning and Inference, 26(2), 131–148.
5. Joseph, V.R., Hung, Y., 2008. Orthogonal-maximin Latin Hypercube designs. Stat Sinica, 18(1), 171–186.
6. Kennedy, M., O’Hagan, A., 2000. Predicting the output from a complex computer code when fast approximations are available. Biometrika, 87(1), 1–13.
7. Loeppky, J.L., Sacks, J., Welch, W.J., 2009. Choosing the sample size of a computer experiment: A practical guide. Technometrics, 51(4), 366–376.
8. Maruri-Aguilar, H., 2010. Personal communication.Google Scholar
9. McKay, M., Beckman, R., Conover, W., 1979. A comparison of three methods for selecting values of input variables in the analysis of output from a computer code. Technometrics, 21(2), 239–245.
10. Niederreiter, H., 1992. Random number generation and quasi-Monte Carlo methods. In CBMSNSF Regional Conference Series in Applied Mathematics, Volume 63, Philadelphia. SIAM.Google Scholar
11. O’Hagan, 2006. Bayesian analysis of computer code output: A tutorial. Reliability Engineering and System Safety, 91, 1290–1300.
12. Owen, A., 1992. Orthogonal arrays for computer experiments, integration and visualization. Stat Sinica, 2(2), 439–452.
13. Qian, P.Z.G., 2009. Nested Latin Hypercube designs. Biometrika, 96(4), 957–970.
14. Qian, P.Z.G., Wu, C.F.J., 2009. Sliced space-filling designs. Biometrika, 96(4), 945–956.
15. Qian, P.Z.G., Wu, H., Wu, C.F.J., 2008. Gaussian process models for computer experiments with qualitative and quantitative factors. Technometrics, 50(3), 383–396.
16. R Development Core Team, 2010. R: A Language and Environment for Statistical Computing. R Foundation for Statistical Computing, Vienna, Austria.Google Scholar
17. Santner, T.J., Williams, B.J., Notz, W.I., 2003. The design and analysis of computer experiments. Springer Verlag, New York.
18. Sobol, L., 1967. 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.