发表机构
University of Edinburgh Business School; Faculty of Science and Engineering, University of Nottingham Ningbo China; College of Data Science, Jiaxing University（爱丁堡大学商学院; 宁波诺丁汉大学理学院; 嘉兴大学数据科学学院）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
研究异位多输出高斯过程中联合多元克里金法是否更优的问题，引入无模型诊断方法，推导预测增益恒等式，证明跨输出依赖性可估计性受特定质量控制，结合结果形成净效益标准并通过实验等给出实际指导。
AI 中文摘要
模拟实验、多保真计算机模型和监测网络经常会产生在不同输入位置观测到的几个相关输出，这是一种称为异位的采样模式。联合多元克里金元模型是否比单独的单变量元模型预测得更好仍未得到解决：在常见设计上进行的仔细模拟比较表明，多元克里金法几乎没有或没有益处，但多保真和地质统计学文献是基于辅助输出有帮助这一前提构建的。我们表明，对于可分离的多输出高斯过程，答案由特定于输出的设计的几何形状决定。我们引入了在拟合前可以计算的无模型诊断方法，即定向覆盖率、定向接近度和借用潜力指数。我们推导了联合建模的神谕预测增益的精确恒等式，并在径向函数下使用局部几何形状对该增益进行了界定。我们进一步证明，跨输出依赖性的可估计性由核加权交叉设计相互作用质量控制，并将这一结果逐个分量地扩展到共区域化线性模型。一个结果是，即使交错设计和分离设计的重叠都为零，它们在统计上也不等价。我们将这些结果结合成一个一阶净效益标准，用于决定何时联合建模是值得的。受控合成实验、一个M/M/1排队示例以及一个多污染物监测网络的案例研究将这一标准转化为实际指导。
英文摘要
We investigate when multivariate kriging improves on separate prediction, using separable multi-output Gaussian processes as the principal theoretical benchmark. We introduce directed coverage, directed proximity and borrowing potential indices to describe design complementarity beyond exact overlap without response values. Under common radial kernels, we derive finite-design bounds linking geometry to prediction gains with known covariance parameters and information for estimating cross-output dependence. An exact risk decomposition under correct specification separates oracle gains from differences in estimation penalties; we give a mean-square expansion under explicit conditions. We distinguish parameter sharing from response coupling: auxiliary data can improve prediction through shared-scale estimation even when direct borrowing is negligible. This distinction guides a calibrated screening-and-validation procedure comparing separate marginal models, a shared-scale independent model and a coupled model, retaining the shared-scale option when coupling is excluded. In simulations with sparse target data and auxiliary observations retained during validation, the procedure reduces mean latent squared-error risk by 6.66% relative to separate fitting. After calibration, screening reduces runtime by 14.01% relative to direct validation of the same candidates, with similar mean risk. Controlled experiments show that covariance misspecification can reverse fitted gains, while queueing and monitoring applications demonstrate the importance of auxiliary coverage and the prediction task. These findings support task-matched validation and separate assessments of predictive accuracy, uncertainty calibration and computational cost.
