This article discusses prior distributions for the parameters of Gaussian processes (GPs) that are widely used as surrogate models to emulate expensive computer simulations. The parameters typically involve mean parameters, a variance parameter, and correlation parameters. These parameters are often estimated by maximum likelihood (MLE). In some scenarios, however, the MLE can be unstable, particularly when the number of simulation runs is small, and some Bayesian estimators display better properties. We introduce default Bayesian priors for the parameters of GPs with isotropic and separable correlation functions for emulating computer simulations with both scalar-valued and vector-valued outputs. We also summarize recent developments of Bayesian priors for calibrating computer models by field or experimental observations. Finally, we review software packages for computer model emulation and calibration.

翻译：本文讨论了高斯过程（GPs）参数先验分布的相关问题，高斯过程作为替代模型被广泛用于仿真昂贵的计算机模拟。这些参数通常包括均值参数、方差参数和相关参数。这些参数通常通过最大似然估计（MLE）进行估计。然而在某些情况下，当模拟运行次数较少时，MLE可能不稳定，而一些贝叶斯估计器表现出更好的性质。我们针对具有各向同性和可分离相关函数的高斯过程参数，提出了用于仿真标量输出和向量输出计算机模拟的默认贝叶斯先验。我们还总结了通过现场或实验观测来校准计算机模型的贝叶斯先验的最新进展。最后，我们回顾了用于计算机模型仿真与校准的软件包。