Bayesian Projected Calibration of Computer Models
Bayesian Projected Calibration of Computer Models
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DOI：
10.1080/01621459.2020.1753519
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发表时间：
2018-03
影响因子：
3.7
通讯作者：
Fangzheng Xie;Yanxun Xu
中科院分区：
文献类型：
--
作者：
Fangzheng Xie;Yanxun Xu
摘要本文提出了一种贝叶斯方法，即贝叶斯投影校准方法，用于解决利用未知复杂物理系统的观测数据校准不完美计算机模型的问题。校准参数和物理系统通过L2投影以可识别的方式参数化。物理系统被施加一个高斯过程先验分布，通过L2投影约束，自然地诱导出校准参数的先验分布。校准参数估计通过其后验分布，作为一个自然的和非渐近的方法的不确定性量化。我们提供了严格的大样本的理由，所提出的方法，通过建立渐近正态性的有效协方差矩阵的校准参数的后验。在理论分析的基础上，设计了两种基于随机逼近的计算算法，并给出了有力的理论支持。通过广泛的模拟研究和两个现实世界的数据集的分析，我们表明，所提出的贝叶斯投影校准可以准确地估计校准参数，校准计算机模型，以及相比，有利的替代方法。本文的补充材料可在网上查阅。
Abstract We develop a Bayesian approach called the Bayesian projected calibration to address the problem of calibrating an imperfect computer model using observational data from an unknown complex physical system. The calibration parameter and the physical system are parameterized in an identifiable fashion via the L 2-projection. The physical system is imposed a Gaussian process prior distribution, which naturally induces a prior distribution on the calibration parameter through the L 2-projection constraint. The calibration parameter is estimated through its posterior distribution, serving as a natural and nonasymptotic approach for the uncertainty quantification. We provide rigorous large sample justifications of the proposed approach by establishing the asymptotic normality of the posterior of the calibration parameter with the efficient covariance matrix. In addition to the theoretical analysis, two convenient computational algorithms based on stochastic approximation are designed with strong theoretical support. Through extensive simulation studies and the analyses of two real-world datasets, we show that the proposed Bayesian projected calibration can accurately estimate the calibration parameters, calibrate the computer models well, and compare favorably to alternative approaches. Supplementary materials for this article are available online.