Objective Bayesian Analysis of a Cokriging Model for Hierarchical Multifidelity Codes
Objective Bayesian Analysis of a Cokriging Model for Hierarchical Multifidelity Codes
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分层多保真代码协同克里金模型的客观贝叶斯分析
DOI：
10.1137/19m1289893
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发表时间：
2019
期刊：
影响因子：
--
通讯作者：
P. Ma
中科院分区：
文献类型：
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作者：
P. Ma
自回归协克里格模型已被广泛用于模拟具有不同保真度水平的多个计算机模型。依赖结构通过高斯过程在每个保真度水平上建模，其中协方差结构通常被参数化为几个参数。预测分布通常需要密集的蒙特卡罗近似在以前的作品。本文推导了仅依赖于相关参数的自回归协克里格模型中预测分布均值和方差的新的闭合公式。对于参数估计，我们考虑这样的自回归协克里格模型的客观贝叶斯分析。我们发现，常见的先验分布的选择，如常数先验和逆相关先验，通常会导致不适当的后验。我们还开发了几个客观的先验，如独立的参考先验和独立的Jeffreys先验，产生适当的后验分布。这种发展是说明与钻孔功能在一个八维输入空间，并应用到一个工程应用中的六维输入空间。补充材料中提供了R代码，用于重现数值结果。
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 require 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. R codes are available in the Supplementary Material to reproduce the numerical results.