SIAM/ASA Journal on Uncertainty Quantification, Volume 8, Issue 4, Page 1358-1382, January 2020.
Autoregressive cokriging models have been widely used to emulate multiple computer models with different levels of fidelity. The dependence structures are modeled via Gaussian processes at each level of fidelity, where covariance structures are often parameterized up to a few parameters. The predictive distributions typically required intensive Monte Carlo approximations in previous works. This article derives new closed-form formulas to compute the means and variances of predictive distributions in autoregressive cokriging models that only depend on correlation parameters. For parameter estimation, we consider objective Bayesian analysis of such autoregressive cokriging models. We show that common choices of prior distributions, such as the constant prior and inverse correlation prior, typically lead to improper posteriors. We also develop several objective priors such as the independent reference prior and the independent Jeffreys prior that are shown to yield proper posterior distributions. This development is illustrated with a borehole function in an eight-dimensional input space and applied to an engineering application in a six-dimensional input space.

中文翻译：

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分层多保真码的协同克里金模型的客观贝叶斯分析

SIAM / ASA不确定性量化期刊，第8卷，第4期，第1358-1382页，2020年1月。
自回归协同克里金模型已被广泛用于模拟具有不同保真度的多个计算机模型。在每个保真度级别上都通过高斯过程对依赖关系结构进行建模，其中协方差结构通常被参数化为几个参数。在以前的工作中，预测分布通常需要密集的蒙特卡洛近似。本文导出了新的闭式公式，以计算仅依赖于相关参数的自回归协同克里金模型中的预测分布的均值和方差。对于参数估计，我们考虑了这种自回归协同克里格模型的客观贝叶斯分析。我们表明，先验分布的常见选择（例如恒定先验和逆相关先验）通常会导致不正确的后验。我们还开发了一些客观先验，例如独立参考先验和独立Jeffreys先验，这些先验被证明可以产生适当的后验分布。在八维输入空间中通过钻孔功能说明了这种发展，并在六维输入空间中将其应用于工程应用。