具有定性和定量因素的计算机实验的双重耦合设计
Doubly Coupled Designs for Computer Experiments with both Qualitative and Quantitative Factors
摘要：
在许多科学和工程应用中，经常会出现定性和定量输入变量的计算机实验。如何选择输入设置是进行准确的统计分析、不确定度量化和决策的重要问题。切片拉丁超立方体设计是第一个系统的方法来解决这个问题。然而，它伴随着与越来越多的定性因素的水平组合相关的成本增加。为了节省试验规模，提出了边际耦合设计，其中定量因素的设计是关于每个定性因素的切片拉丁超立方体设计。这种设计的缺点是，相应的数据可能无法捕捉任何两个（和更多）定性因素和定量因素之间的影响。为了平衡试验规模和设计效率，我们提出了一种新的设计类型，双耦合设计，其中定量因素的设计点形成一个切片拉丁超立方体设计的任何定性因素的水平和任何两个定性因素的水平组合，分别。与边缘耦合设计相比，所提出的设计在定性和定量因素之间具有更好的分层性。所提出的设计的存在是成立的。介绍了几种构造方法，并对所得设计的性质进行了研究。
英文摘要：
Computer experiments with both qualitative and quantitative input variables occur frequently in many scientific and engineering applications. How to choose input settings for such experiments is an important issue for accurate statistical analysis, uncertainty quantification and decision making. Sliced Latin hypercube designs are the first systematic approach to address this issue. However, it comes with the increasing cost associated with an increasing large number of level combinations of the qualitative factors. For the reason of run size economy, marginally coupled designs were proposed in which the design for the quantitative factors is a sliced Latin hypercube design with respect to each qualitative factor. The drawback of such designs is that the corresponding data may not be able to capture the effects between any two (and more) qualitative factors and quantitative factors. To balance the run size and design efficiency, we propose a new type of designs, doubly coupled designs, where the design points for the quantitative factors form a sliced Latin hypercube design with respect to the levels of any qualitative factor and with respect to the level combinations of any two qualitative factors, respectively. The proposed designs have the better stratification property between the qualitative and quantitative factors compared with marginally coupled designs. The existence of the proposed designs is established. Several construction methods are introduced, and the properties of the resulting designs are also studied.
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