Computer Experiments With Both Qualitative and Quantitative Variables

Computer experiments have received a great deal of attention in many fields of science and technology. Most literature assumes that all the input variables are quantitative. However, researchers often encounter computer experiments involving both qualitative and quantitative variables (BQQV). In this paper, a new interface on design and analysis for computer experiments with BQQV is proposed. The new designs are one kind of sliced Latin hypercube designs with points clustered in the design region, and possess good uniformity for each slice. For computer experiments with BQQV, such designs help to measure the similarities among responses of different level-combinations in the qualitative variables. An adaptive analysis strategy intended for the proposed designs is developed. The proposed strategy allows us to automatically extract information from useful auxiliary responses to increase the precision of prediction for the target response. The interface between the proposed design and the analysis strategy is demonstrated to be effective via simulation and a real-life example from the food engineering literature. This article has supplementary material online.

计算机实验已在诸多科技领域受到广泛关注。现有绝大多数文献均假设所有输入变量均为定量变量，但研究人员在实际研究中时常会遇到同时包含定性与定量变量（BQQV）的计算机实验场景。本文针对含BQQV的计算机实验，提出一套全新的设计与分析框架：所提设计属于一类在设计区域内存在点簇的切片拉丁超立方设计（sliced Latin hypercube designs），且各切片均具备良好的空间均匀性。针对此类实验场景，该类设计可有效量化定性变量不同水平组合下各响应间的相似性。本文同时开发了适配该类设计的自适应分析策略，该策略能够自动从有效辅助响应中提取信息，以提升目标响应的预测精度。经仿真实验与食品工程领域的真实案例验证，本文所提设计与分析策略的适配框架具备良好有效性。本文附带在线补充材料。