In the past decades computer experiments or computer-based simulation have become a hot topic in statistics and engineering. The uniform experimental design (UD for short) proposed by Fang and Wang (Fang 1980; Wang and Fang 1981) is one of the space-filling designs for computer experiments and is also one of robust designs for experiments with model uncertainty. Suppose that there are s factors, X 1, …, X s , in an experiment. The experimental region of the factors is denoted by \(\mathcal{T}\), very often, \(\mathcal{T}\) is a rectangle [a 1, b 1] ×⋯ ×[a s , b s ]. From now on we always assume \(\mathcal{T}\) to be a rectangle. Without any generality we can assume that \(\mathcal{T}\) is a unit cube, [0, 1]s, in the space R s. A uniform design is a set of points that are uniformly scattered over the region \(\mathcal{T}\) in a certain sense.
Consider the problem of estimating the response (y) as a function of several controlled factors (X 1, …, X s ) in a computer experiment. The true...
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References and Further Reading
Fang KT (1980) The uniform design: application of number-theoretic methods in experimental design, Acta Math Appl Sin 3:363–372
Fang KT, Li R, Sudjianto A (2005) Design and modeling for computer experiments. Chapman & Hall/CRC, London
Fang KT, Lin DKJ (2003) Uniform designs and their application in industry. In: Khattree R, Rao CR (eds) Handbook on statistics 22: statistics in industry. Elsevier/North-Holland, Amsterdam, pp 131–170
Fang KT Lin DKJ, Winker P, Zhang Y (2000) Uniform design: theory and applications. Technometrics 42:237–248
Fang KT, Wang Y (1994) Number-theoretic methods in statistics. Chapman and Hall, London
Hickernell FJ (1998) A generalized discrepancy and quadrature error bound. Math Comp 67:299–322
McKay MD, Beckman RJ, Conover WJ (1979) A comparison of three methods for selecting values of input variables in the analysis of output from a computer code. Technometrics 21:239–245
Wang Y, Fang KT (1981) A note on uniform distribution and experimental design. Chin Sci Bull 26:485–489
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Fang, KT. (2011). Uniform Experimental Design. In: Lovric, M. (eds) International Encyclopedia of Statistical Science. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-04898-2_601
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