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：模型标定是指利用实验或现场数据估计数学模型中的未知参数。数据中存在的模型偏差和测量偏差使该任务复杂化。例如，卫星干涉图常用于地质灾害量化中地球物理模型的标定。本研究利用卫星干涉图将地表形变观测与夏威夷基拉韦厄火山岩浆房属性建立关联。我们推导出闭式边缘似然函数，并实现了同时估计物理模型偏差及卫星干涉图大气误差引起的测量偏差的后验采样程序。研究发现，相较于基于多数据集的标定方法，通过聚合多幅干涉图并降采样像素进行模型标定可降低计算复杂度。本研究分析了数据聚合与降采样操作不造成信息损失的条件。仿真实验表明偏差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。我们将相关计算工具实现于CRAN平台上的RobustCalibration软件包中。