计算机实验中均匀性检验与可视化的雷达形统计量
A Radar-Shaped Statistic for Testing and Visualizing Uniformity Properties in Computer Experiments
摘要：
在计算机代码的研究中，尽可能均匀地填充空间对于描述所研究现象的复杂性是很重要的。然而，这种性质并不通过减少维度来保持。一些数值试验设计在这个意义上被认为是拉丁超立方体或正交表，但它们只考虑到轴或坐标平面上的投影。在这篇文章中，我们介绍了一个统计，它允许研究良好的分布点，根据所有的1维投影。通过有角度地扫描域，我们得到一个雷达型表示，允许的均匀性缺陷的设计，以确定其在直线上的投影。这种新工具的优点，通常的例子空间填充设计（SFD）和独立的旋转角度的全局统计进行了研究。
英文摘要：
In the study of computer codes, filling space as uniformly as possible is important to describe the complexity of the investigated phenomenon. However, this property is not conserved by reducing the dimension. Some numeric experiment designs are conceived in this sense as Latin hypercubes or orthogonal arrays, but they consider only the projections onto the axes or the coordinate planes. In this article we introduce a statistic which allows studying the good distribution of points according to all 1-dimensional projections. By angularly scanning the domain, we obtain a radar type representation, allowing the uniformity defects of a design to be identified with respect to its projections onto straight lines. The advantages of this new tool are demonstrated on usual examples of space-filling designs (SFD) and a global statistic independent of the angle of rotation is studied.
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