<p>Lecture 7: “Deterministic” Sampling</p><p>Recommended Books: • Box, G.E.; Hunter, J.S., Hunter,W.G. (2005). Statistics for Experimenters: Design, Innovation, and Discovery, 2nd Edition. Wiley. • NIST Engineering Statistics Handbook: http://www.itl.nist.gov/div898/handbook/index.htm • A. S. Hedayat, N. J. A. Sloane and John Stufken. Orthogonal Arrays: Theory and Applications. Springer-Verlag, New York. 1999. • D. E. Knuth. The Art of Computer Programming, Vol. 2: Seminumerical Algorithms, 3rd ed. Addison-Wesley, 1998. • R. H. Myers and D. C. Montgomery. Response Surface Methodology: Process and Product Optimization Using Designed Experiments. John Wiley & Sons, Inc., New York, 1995. • T.J. Santner, B. J. Williams, and W. I. Notz. The Design and Analysis of Computer Experiments. Springer-Verlag, New York: 1993.</p><p>Recommended Articles: • Paul Bratley, Bennett Fox, Harald Niederreiter. Implementation and Tests of Low Discrepancy Sequences, ACM Transactions on Modeling and Computer Simulation, Volume 2, Number 3, July 1992, pages 195-213. • Harald Niederreiter, Random Number Generation and quasi-Monte Carlo Methods, SIAM, 1992. • Halton, J. H. "On the efficiency of certain quasi-random sequences of points in evaluating multi-dimensional integrals, Numerische Mathematik,Volume 2 pages 84-90. • Kocis, L. and W. Whiten, 1997. "Computational Investigations of Low- Discrepancy Sequences," ACM Transactions on Mathematical Software, Volume 23, Number 2, 1997, pages 266-294. • Robinson, D.G. and C. Atcitty, 1999. "Comparison of Quasi- and Pseudo-Monte Carlo Sampling for Reliability and Uncertainty Analysis." Proceedings of the AIAA Probabilistic Methods Conference, St. Louis MO, AIAA99-1589. • Romero, Vicente J., Raisa Slepoy, Laura P. Swiler, Anthony A. Giunta, T. Krishnamurthy, "Error Estimation Approaches for Progressive Response Surfaces," Conference Paper, AIAA/ASME/ASCE/AHS/ASC 35th Structures, Structural Dynamics, and Materials Conference, April 2005. • Swiler, Laura P, Raisa Slepoy, Anthony A Giunta, "Evaluation of Sampling Methods in Constructing Response Surface Approximations," Conference Paper, AIAA SDM NonDeterministic Approaches Conference, May 2006. • Sacks et al., 1989. J. Sacks, S. Schiller and W. Welch. Designs for computational experiments. Technometrics 31 (1989), pp. 41–47. • M. D. Morris. Factorial sampling plans for preliminary computational experiments. Technometrics, 33(2):161–174, 1991. • Q. Du, V. Faber, and M. Gunzburger. Centroidal voronoi tessellations: Applications and algorithms. SIAM Review, 41:637–676, 1999. • Vicente Romero, John Burkardt, Max Gunzburger, Janet Peterson. Initial Evaluation of Pure and "Latinized" Centroidal Voronoi Tessellation for Non- Uniform Statistical Sampling, Sensitivity Analysis of Model Output (SAMO 2004) Conference, Santa Fe, March 8-11, 2004.</p>