A generalized discrepancy and quadrature error bound
Mathematics of Computation
Could Enough Samples be more Important than Better Designs for Computer Experiments?
ANSS '05 Proceedings of the 38th annual Symposium on Simulation
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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.