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A fast and calibrated computer model emulator: an empirical Bayes approach

机译：一个快速和校准的计算机模型仿真器：经验贝叶斯方法

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摘要

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.
机译：在计算机上实现的数学模型已成为科学过程循环加速背后的驱动力。这是因为计算机模型通常比物理实验更快，经济得多。在这项工作中，我们使用计算机模型开发了一个经验贝叶斯方法，以使用计算机模型预测物理量的预测，我们假设需要校准所考虑的计算机模型，并计算昂贵。我们提出了一种高斯工艺仿真器和高斯过程模型，用于计算机模型与底层物理过程之间的系统差异。这允许通过高斯过程引起的条件分布给出的闭合形式和易于计算的预测。我们通过建立估计物理过程的后验一致性提供了拟议的方法的严格理论基化。在广泛的仿真研究和实际数据示例中，证明了该方法的计算效率。新建立的方法从实际和理论上的立场中提高了计算机模型的使用。

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