Model calibration consists of using experimental or field data to estimate the unknown parameters of a mathematical model. The presence of model discrepancy and measurement bias in the data complicates this task. Satellite interferograms, for instance, are widely used for calibrating geophysical models in geological hazard quantification. In this work, we used satellite interferograms to relate ground deformation observations to the properties of the magma chamber at K\={\i}lauea Volcano in Hawai`i. We derived closed-form marginal likelihoods and implemented posterior sampling procedures that simultaneously estimate the model discrepancy of physical models, and the measurement bias from the atmospheric error in satellite interferograms. We found that model calibration by aggregating multiple interferograms and downsampling the pixels in the interferograms can reduce the computation complexity compared to calibration approaches based on multiple data sets. The conditions that lead to no loss of information from data aggregation and downsampling are studied. Simulation illustrates that both discrepancy and measurement bias can be estimated, and real applications demonstrate that modeling both effects helps obtain a reliable estimation of a physical model's unobserved parameters and enhance its predictive accuracy. We implement the computational tools in the RobustCalibration package available on CRAN.

翻译：模型校准是指利用实验或现场数据估算数学模型中未知参数的过程。模型差异与数据测量偏差的存在使该任务复杂化。例如，卫星干涉图广泛用于地质灾害定量化研究中对地球物理模型的校准。本研究利用卫星干涉图将夏威夷基拉韦厄火山的地表形变观测与岩浆房特征参数相关联。我们推导了闭式边缘似然函数，并实施后验采样程序，该程序可同时估计物理模型的模型差异以及卫星干涉图中大气误差引起的测量偏差。研究发现，与基于多数据集校准方法相比，通过聚合多个干涉图及对像素进行降采样进行模型校准可降低计算复杂度。本文探讨了数据聚合与降采样不造成信息损失的条件。模拟实验表明差异与测量偏差均可被估计，实际应用证明同时建模这两种效应有助于可靠估计物理模型的未观测参数并提升预测精度。我们已在CRAN平台发布的RobustCalibration软件包中实现了相关计算工具。