变换的低偏差设计也是低偏差设计吗？
Is a Transformed Low Discrepancy Design Also Low Discrepancy?
AI总结：
本文探讨变换均匀设计是否仍保持低偏差特性，分析了核函数条件对结果的影响，并提出优化方法。
摘要：
旨在匹配任意目标分布的实验设计通常通过变量变换构造。偏差是衡量经验分布与目标分布匹配程度的指标。本文探讨变换低偏差均匀设计是否仍为低偏差设计。答案取决于所用的两个核函数。若满足特定条件，则答案为是。但这些条件可能在实际中不适用。此时变换后的设计可能具有较大偏差。本文通过示例说明此现象，并提出解决方案，如确保原始设计的一维投影最优，或使用坐标交换算法优化偏差。
英文摘要：
Experimental designs intended to match arbitrary target distributions are typically constructed via a variable transformation of a uniform experimental design. The inverse distribution function is one such transformation. The discrepancy is a measure of how well the empirical distribution of any design matches its target distribution. This chapter addresses the question of whether a variable transformation of a low discrepancy uniform design yields a low discrepancy design for the desired target distribution. The answer depends on the two kernel functions used to define the respective discrepancies. If these kernels satisfy certain conditions, then the answer is yes. However, these conditions may be undesirable for practical reasons. In such a case, the transformation of a low discrepancy uniform design may yield a design with a large discrepancy. We illustrate how this may occur. We also suggest some remedies. One remedy is to ensure that the original uniform design has optimal one-dimensional projection, but this remedy works best if the design is dense, or in other words, the ratio of sample size divided by the dimension of the random variable is relatively large. Another remedy is to use the transformed design as the input to a coordinate-exchange algorithm that optimizes the desired discrepancy, and this works for both dense or sparse designs. The effectiveness of these two remedies is illustrated via simulation.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
