ABSTRACT
Sampling uniformity is one of the central issues for computer experiments or metamodeling. Is it generally true that more uniformly distributed sampling leads to more accurate prediction? A study was conducted to compare four designs for computer experiments, based on simulation tests and statistical analysis. Maximin Latin hypercube design (LHMm) nearly always generated more uniform sampling in two- and three- dimensional cases than does random sampling (Rd), Latin hypercube design (LHD), or Minimized centered L2 discrepancy Latin hypercube design (LHCL2). But often there was no significant difference among the means of the prediction errors by employing LHMm versus the other designs. Occasionally, even the opposite was seen. More uniform sampling did not generally lead to more accurate prediction unless sampling included extremely nonuniform cases, especially when the sample size was relatively small.
- Hickernell, F. J. K (1998): A generalized discrepancy and quadrature error bound, Mathematics of Computation, 67, 299--322. Google ScholarDigital Library
- Koehler, J. R., Owen, A. B. 1996: Computer experiments. In Ghosh, S. and Rao, C. R., editors, Handbook of Statistics, 13, 261--308. Elsevier Science, New York.Google ScholarCross Ref
- Liu, L., 2004: Employing simulation and optimizer to optimize experimental design and structural topology, dissertation, Systems Science Ph.D. Program, Portland State University.Google Scholar
- Liu, L., 2005: Could enough samples be more important than better designs for computer experiments? 38th Annual Simulation Symposium, Spring Simulation Multiconference, San Diego, April 2--8, 2005. Google ScholarDigital Library
- Morris, M. D. and Mitchell, T. J., 1995, "Exploratory Designs for Computer Experiments," Journal of Statistical Planning and Inference, 43, 381--402.Google ScholarCross Ref
- Nielsen, H. B., Lophaven, S. N., and Søndergaard, J.: DACE: A MATLAB KrigingToolbox <http://www.imm.dtu.dk/~hbn/dace>Google Scholar
- Santner, T., Williams, B, and Notz, W. 2003: Design and Analysis of Computer Experiments, Springer-Verlag, New York.Google Scholar
- Does more uniformly distributed sampling generally lead to more accurate prediction in computer experiments?
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