Computer experiments involving both qualitative and quantitative (QQ) factors have attracted increasing attention. Gaussian process (GP) models have proven effective in this context by choosing specialized covariance functions for QQ factors. In this work, we extend the latent variable-based GP approach, which maps qualitative factors into a continuous latent space, by establishing a general framework to apply standard kernel functions to continuous latent variables. This approach provides a novel perspective for interpreting some existing GP models for QQ factors and introduces new covariance structures in some situations. The ordinal structure can be incorporated naturally and seamlessly in this framework. Furthermore, the Bayesian information criterion and leave-one-out cross-validation are employed for model selection and model averaging. The performance of the proposed method is comprehensively studied on several examples.

翻译：涉及定性与定量（QQ）因素的计算机实验日益受到关注。高斯过程（GP）模型通过为QQ因素选择专用协方差函数，已被证明在此类场景中具有良好效果。本研究通过建立通用框架将标准核函数应用于连续潜变量，扩展了基于潜变量的GP方法（该方法将定性因素映射至连续潜空间）。该框架为解读现有QQ因素GP模型提供了新视角，并在特定场景下引入了新的协方差结构。序数结构可在此框架中实现自然无缝的整合。此外，研究采用贝叶斯信息准则与留一交叉验证进行模型选择与模型平均。通过多个算例对提出方法的性能进行了综合评估。