Journal
TECHNOMETRICS
Volume 52, Issue 4, Pages 421-429Publisher
AMER STATISTICAL ASSOC
DOI: 10.1198/TECH.2010.09157
Keywords
Arc-sine distribution; Logarithmic potential; Space-filling designs; Uniform designs
Categories
Funding
- Collaborative Research Center of the German Research Foundation (DFG) [SFB 823]
- NIH [IR01GM072876:01A1]
- EPSRC [EP/D048893/1]
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Space filling designs, which satisfy a uniformity property, are widely used in computer experiments. In the present paper, the performance of nonuniform experimental designs, which locate more points in a neighborhood of the boundary of the design space, is investigated. These designs are obtained by a quantile transformation of the one-dimensional projections of commonly used space-filling designs. This transformation is motivated by logarithmic potential theory, which yields the arc-sine measure as an equilibrium distribution. The methodology is illustrated for maximin Latin hypercube designs by several examples. In particular, it is demonstrated that the new designs yield a smaller integrated mean squared error for prediction.
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