A fast and calibrated computer model emulator: an empirical Bayes approach
A fast and calibrated computer model emulator: an empirical Bayes approach
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DOI：
10.1007/s11222-021-10024-8
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发表时间：
2020-08
影响因子：
2.2
通讯作者：
Vojtech Kejzlar;Mookyong Son;Shrijita Bhattacharya;T. Maiti
中科院分区：
文献类型：
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作者：
Vojtech Kejzlar;Mookyong Son;Shrijita Bhattacharya;T. Maiti
在计算机上实现的数学模型已经成为加速科学过程周期的驱动力。这是因为计算机模型通常比物理实验运行得更快和更经济。在这项工作中，我们开发了一种经验贝叶斯方法，使用计算机模型来预测物理量，我们假设所考虑的计算机模型需要校准，并且计算成本很高。我们提出了一个高斯过程仿真器和高斯过程模型的计算机模型和底层物理过程之间的系统差异。这允许由高斯过程引起的条件分布给出的封闭形式和易于计算的预测。我们提供了一个严格的理论依据所提出的方法，通过建立后验的一致性估计的物理过程。在一个广泛的模拟研究和一个真实的数据的例子证明了该方法的计算效率。新建立的方法从实践和理论的角度加强了计算机模型的使用。
Mathematical models implemented on a computer have become the driving force behind the acceleration of the cycle of scientific processes. This is because computer models are typically much faster and economical to run than physical experiments. In this work, we develop an empirical Bayes approach to predictions of physical quantities using a computer model, where we assume that the computer model under consideration needs to be calibrated and is computationally expensive. We propose a Gaussian process emulator and a Gaussian process model for the systematic discrepancy between the computer model and the underlying physical process. This allows for closed-form and easy-to-compute predictions given by a conditional distribution induced by the Gaussian processes. We provide a rigorous theoretical justification of the proposed approach by establishing posterior consistency of the estimated physical process. The computational efficiency of the methods is demonstrated in an extensive simulation study and a real data example. The newly established approach makes enhanced use of computer models both from practical and theoretical standpoints.