SIAM/ASA Journal on Uncertainty Quantification, Volume 8, Issue 1, Page 1-26, January 2020.
Weakly stationary Gaussian processes (GPs) are the principal tools in the statistical approaches to the design and analysis of computer experiments (or uncertainty quantification). Such processes are fitted to computer model output using a set of training runs to learn the parameters of the process covariance kernel. The stationarity assumption is often adequate, yet can lead to poor predictive performance when the model response exhibits nonstationarity, for example, if its smoothness varies across the input space. In this paper, we introduce a diagnostic-led approach to fitting nonstationary GP emulators by specifying finite mixtures of region-specific covariance kernels. Our method first fits a stationary GP and, if traditional diagnostics exhibit nonstationarity, those diagnostics are used to fit appropriate mixing functions for a covariance kernel mixture designed to capture the nonstationarity, ensuring an emulator that is continuous in parameter space and readily interpretable. We compare our approach to the principal nonstationary GP models in the literature and illustrate its performance on a number of idealized test cases and in an application to modeling the cloud parameterization of the French climate model.

中文翻译：

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诊断驱动的非平稳仿真器，使用内核混合物

SIAM / ASA不确定性量化杂志，第8卷，第1期，第1-26页，2020年1月。
静态平稳的高斯过程（GPs）是计算机实验（或不确定性量化）的设计和分析的统计方法中的主要工具。使用一组训练运行将这些过程拟合到计算机模型输出，以学习过程协方差内核的参数。平稳性假设通常是足够的，但是当模型响应表现出非平稳性时（例如，如果其平滑度在整个输入空间中变化），则可能导致较差的预测性能。在本文中，我们通过指定特定于区域的协方差内核的有限混合，引入了一种诊断主导的方法来拟合非平稳GP模拟器。我们的方法首先适合固定的GP，如果传统诊断显示不稳定，这些诊断程序用于为协方差内核混合拟合合适的混合函数，以捕获非平稳性，从而确保仿真器在参数空间中连续且易于解释。我们将我们的方法与文献中的主要非平稳GP模型进行了比较，并在许多理想的测试案例上以及在对法国气候模型的云参数化建模的应用中说明了其性能。