论文标题
快速校准的计算机模型模拟器：经验贝叶斯方法
A Fast and Calibrated Computer Model Emulator: An Empirical Bayes Approach
论文作者
论文摘要
在计算机上实施的数学模型已成为加速科学过程加速的推动力。这是因为计算机模型通常比物理实验要快得多，运行。在这项工作中，我们开发了一种经验贝叶斯的方法来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，并且计算上的昂贵。我们提出了一个高斯过程模拟器和一个高斯过程模型，以实现计算机模型与基础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封闭形式和易于计算的预测。我们通过建立估计的物理过程的后验一致性来对所提出的方法提供严格的理论理由。该方法的计算效率在广泛的模拟研究和真实数据示例中得到了证明。从实际和理论的角度来看，新建立的方法可以增强计算机模型的使用。
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.
