论文标题
在还原模型不确定性下，大规模贝叶斯线性反问题的最佳设计：很高兴知道您不知道的
Optimal design of large-scale Bayesian linear inverse problems under reducible model uncertainty: good to know what you don't know
论文作者
论文摘要
我们考虑了由偏微分方程控制的无限维贝叶斯线性反问题的最佳设计，该方程除了反转参数的不确定性外，还包含次要还原模型不确定性。通过可简化的不确定性，我们指的是可以通过参数推断降低的参数不确定性。我们寻求实验设计，以最大程度地减少主要参数的后验不确定性，同时考虑了次级参数的不确定性。我们通过得出边缘化的A型标准来实现这一目标，并为其优化开发有效的计算方法。我们说明了我们在污染物传输模型中估算不确定时间依赖性来源的方法，其初始状态为二次不确定性。我们的结果表明，在实验设计过程中考虑其他模型不确定性至关重要。
We consider optimal design of infinite-dimensional Bayesian linear inverse problems governed by partial differential equations that contain secondary reducible model uncertainties, in addition to the uncertainty in the inversion parameters. By reducible uncertainties we refer to parametric uncertainties that can be reduced through parameter inference. We seek experimental designs that minimize the posterior uncertainty in the primary parameters, while accounting for the uncertainty in secondary parameters. We accomplish this by deriving a marginalized A-optimality criterion and developing an efficient computational approach for its optimization. We illustrate our approach for estimating an uncertain time-dependent source in a contaminant transport model with an uncertain initial state as secondary uncertainty. Our results indicate that accounting for additional model uncertainty in the experimental design process is crucial.
