Model misspecification constitutes a major obstacle to reliable inference in many inverse problems. Inverse problems in seismology, for example, are particularly affected by misspecification of wave propagation velocities. In this paper, we focus on a specific seismic inverse problem - full-waveform moment tensor inversion - and develop a Bayesian framework that seeks robustness to velocity misspecification. A novel element of our framework is the use of transport-Lagrangian (TL) distances between observed and model predicted waveforms to specify a loss function, and the use of this loss to define a generalized belief update via a Gibbs posterior. The TL distance naturally disregards certain features of the data that are more sensitive to model misspecification, and therefore produces less biased or dispersed posterior distributions in this setting. To make the latter notion precise, we use several diagnostics to assess the quality of inference and uncertainty quantification, i.e., continuous rank probability scores and rank histograms. We interpret these diagnostics in the Bayesian setting and compare the results to those obtained using more typical Gaussian noise models and squared-error loss, under various scenarios of misspecification. Finally, we discuss potential generalizability of the proposed framework to a broader class of inverse problems affected by model misspecification.
翻译:例如,地震学的反面问题特别受到波浪传播速度的偏差影响。在本论文中,我们侧重于一个具体的地震反向问题――全波式瞬时反转,并开发一个巴伊西亚框架,以寻求对速度偏差的稳健性。我们框架的一个新内容是使用所观测到的和模型预测的波形之间的运输-拉格朗(TL)距离来指定损失函数,以及利用这种损失来界定通过Gibs 海报进行的普遍信仰更新。TL距离自然忽略了数据中某些对模型误差比较敏感的特征,因此在这一背景下产生偏差或分散的海面分布。为了使后一个概念精确化,我们用几种诊断来评估推断和不确定性量化的质量,即,连续的等级概率分数和直方形等。我们用Bayesian设置中的这些诊断方法来解释这些诊断结果,并且用更典型的Gibs 类更新结果来比较那些通过更典型的Gabs