A new class of Latin hypercube designs with high-dimensional hidden projective uniformity

Abstract

Latin hypercube design is a good choice for computer experiments. In this paper, we construct a new class of Latin hypercube designs with some high-dimensional hidden projective uniformity. The construction is based on a new class of orthogonal arrays of strength two which contain higher strength orthogonal arrays after their levels are collapsed. As a result, the obtained Latin hypercube designs achieve higher-dimensional uniformity when projected onto the columns corresponding to higher strength orthogonal arrays, as well as twodimensional projective uniformity. Simulation study shows that the constructed Latin hypercube designs are significantly superior to the currently used designs in terms of the times of correctly identifying the significant effects.

Keywords

Computer experiment / hidden projective uniformity / Latin hypercube design / level-collapsing / orthogonal array

References

[1] Beattie S. D., Lin D. K. J. Fan J., Li G. A new class of Latin hypercubes for computer experiments. Contemporary Multivariate Analysis and Designs of Experiments, in Celebration of Prof. Kai-Tai Fang’s 65th Birthday, 2005, Singapore: World Scientific 205-226

[2] Fang K. T., Li R. Z., Sudjianto A. Design and Modeling for Computer Experiments, 2005, New York: Chapman and Hall/CRC Press

[3] Hedayat A. S., Sloane N. J. A., Stufken J. Orthogonal Arrays: Theory and Applications, 1999, New York: Springer.

[4] Hirschfeld J. W. P. Projective geometries over finite fields, 1998, Oxford: Oxford Univ Press.

[5] Leary S., Bhaskar A., Keane A. Optimal orthogonal-array-based Latin hypercubes. J Appl Stat, 2003, 30, 585-598

[6] Lin C. D., Bingham D., Sitter R. R., Tang B. A new and flexible method for constructing designs for computer experiments. Ann Statist, 2010, 38, 1460-1477

[7] Lin C. D., Mukerjee R., Tang B. Construction of orthogonal and nearly orthogonal Latin hypercubes. Biometrika, 2009, 96, 243-247

[8] 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, 1979, 21, 239-245

[9] Pang F., Liu M. Q., Lin D. K. J. A construction method for orthogonal Latin hypercube designs with prime power levels. Statist Sinica, 2009, 19, 1721-1728

[10] Qian P. Z. G., Ai M. Y. Nested lattice sampling: a new sampling scheme derived by randomizing nested orthogonal arrays. J Amer Statist Assoc, 2010, 105, 1147-1155

[11] Qian P. Z. G., Ai M. Y., Wu C. F. J. Construction of Nested Space-Filling Designs. Ann Statist, 2009, 37, 3616-3643

[12] Ranjan P., Bingham D. R., Dean A. M. Existence and construction of randomization defining contrast subspaces for regular factorial designs. Ann Statist, 2009, 37, 3580-3599

[13] Santner T. J., Williams B. J., Notz W. I. The Design and Analysis of Computer Experiments, 2003, New York: Springer.

[14] Schürer R., Schmid W. C. MinT-Architecture and applications of the (t, m, s)-net and OOA Database. Math Comput Simulation, 2010, 80, 1124-1132

[15] Steinberg M., Lin D. K. J. A construction method for orthogonal Latin hypercube designs. Biometrika, 2006, 93, 279-288

[16] Sun F. S., Liu M. Q., Lin D. K. J. Construction of orthogonal Latin hypercube designs. Biometrika, 2009, 96, 971-974

[17] Tang B. Orthogonal array-based Latin Hypercubes. J Amer Statist Assoc, 1993, 88, 1392-1397

[18] Tang B. A theorem for selecting OA-based Latin hypercubes using a distance criterion. Communications in Statistics-Theory and Methods, 1994, 23, 2047-2058

[19] Wu C. F. J., Hamada M. Experiments: Planning, Analysis and Parameter Design Optimization, 2000, New York: Wiley.

[20] Ye K. Q. Orthogonal column Latin hypercubes and their application in computer experiments. J Amer Statist Assoc, 1998, 93, 1430-1439