Construction Of Uniform Design Under Mixture Discrepancy

As the one of the most important space filling designs, uniform design has been widely used in many areas especially in the computer experiments. A uniform design seeks its design points to be scattered uniformly on the whole experimen-tal domain. Statisticians have proposed many kinds of discrepancies. Among them, most commonly used are the Lp-star discrepancy, the centered discrepancy (CD), the wrap-around L2- discrepancy(WD), the symmetric discrepancy(SD), and the mixture discrepancy(MD) etc. The mixture discrepancy behaves more outstanding than the traditional discrepancies from some aspects such as the intuitive view, the cover frequency, and the curse of dimensionality. Hence it is also important to con-struct uniform design under mixture discrepancy. There are various approaches to construct the uniform design at present, such as the glp method, the threshold accepting(TA) algorithm, the cutting method etc. It is difficult to construct a uni-form design due to the computation complexity when nâ†'∞ or s is large. Ma and Fang (2004) proposed the cutting method for constructing uniform design under CD, SD and Lp- discrepancy. Fang and Qin (2003) proposed the collapsing method for constructing uniform design under CD and WD. Their methods and conclusions are generalized to construct the uniform design under the mixture discrepancy in this paper. The analytic formulas of MD-value between the novel design and the two original designs in the collapsing method are also shown. Both methods have the advantage of less computation load than other methods, and the final uniform design is also nearly uniform design.