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:模型校准包括使用实验或实地数据来估计数学模型的未知参数。数据中存在模型差异和测量偏差使这项任务复杂化。例如,卫星干涉图在地质危害量化中广泛用于校准地球物理模型;在这项工作中,我们使用卫星干涉图将地面变形观测与Hawaiiii 的K<unk> i}lauea Volcano 岩浆室的特性联系起来。我们得出了闭式边际可能性,并实施了后方取样程序,同时估计物理模型的模型差异和卫星干涉图中大气误差的测量偏差。我们发现,通过汇总多个干涉图和下游样图中的像素,模型校准可以降低计算复杂性,而与基于多个数据集的校准方法相比。我们研究了导致数据汇总和下游不丢失信息的条件。模拟表明,可以估计差异和测量偏差,而实际应用则表明,在卫星干涉图中,两种影响都有助于获得对物理模型的未观测到的模型的模型的模型参数进行可靠的估计,并改进CRAN的计算工具的精确性。</s>