Uncertainty Quantification for Computer Models With Spatial Output Using Calibration-Optimal Bases
Uncertainty Quantification for Computer Models With Spatial Output Using Calibration-Optimal Bases
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DOI：
10.1080/01621459.2018.1514306
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发表时间：
2019-03-20
影响因子：
3.7
通讯作者：
Kharin, Viatcheslav
中科院分区：
文献类型：
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作者：
Salter, James M.;Williamson, Daniel B.;Kharin, Viatcheslav
使用不确定度量化（UQ）方法对复杂计算机代码进行校准是统计方法学发展的一个丰富领域。当将这些技术应用于具有空间输出的模拟器时，现在标准的方法是使用主成分分解来降低输出的维度，以便允许高斯过程模拟器预测输出以进行校准。我们引入了“终端情况”，在这种情况下，模型不能再现模型内的观测值差异，并且UQ的标准校准方法不能给出合理的结果。我们表明，即使模型不存在这样的问题，对输出的标准分解也可以并且通常会导致最终案例分析。我们提出了一个简单的测试，允许从业者确定他们的实验是否会导致最终病例分析，以及一种定义校准最佳基础的方法，以避免在不可避免的情况下发生这种情况。我们提出了这样做的最优旋转算法，并证明了它的有效性，为一个理想的例子，通常的主成分方法失败。我们将这些想法应用于CanAM4模式，以演示气候模式产生的终端情况问题。我们在此背景下讨论了气候模式调优和模式差异的估计，并展示了如何将最优旋转算法用于开发实用的气候模式调优工具。这篇文章可以在网上找到。
The calibration of complex computer codes using uncertainty quantification (UQ) methods is a rich area of statistical methodological development. When applying these techniques to simulators with spatial output, it is now standard to use principal component decomposition to reduce the dimensions of the outputs in order to allow Gaussian process emulators to predict the output for calibration. We introduce the "terminal case," in which the model cannot reproduce observations to within model discrepancy, and for which standard calibration methods in UQ fail to give sensible results. We show that even when there is no such issue with the model, the standard decomposition on the outputs can and usually does lead to a terminal case analysis. We present a simple test to allow a practitioner to establish whether their experiment will result in a terminal case analysis, and a methodology for defining calibration-optimal bases that avoid this whenever it is not inevitable. We present the optimal rotation algorithm for doing this, and demonstrate its efficacy for an idealized example for which the usual principal component methods fail. We apply these ideas to the CanAM4 model to demonstrate the terminal case issue arising for climate models. We discuss climate model tuning and the estimation of model discrepancy within this context, and show how the optimal rotation algorithm can be used in developing practical climate model tuning tools. for this article are available online.