Optimal design of large-scale Bayesian linear inverse problems under reducible model uncertainty: good to know what you don't know

The next CMAI Colloquium will be on

Date: Friday, October 16, 2020 at 10am (Eastern Time) 

Speaker: Prof. Noemi Petra 

School of Natural Sciences  

University of California, Merced 

Title: Optimal design of large-scale Bayesian linear inverse problems under reducible model uncertainty: good to know what you don't know

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Abstract     : Optimal experimental design (OED) refers to the task of determining an experimental setup such that the measurements are most informative about the underlying parameters. This is particularly important in situations where experiments are costly or time-consuming, and thus only a small number of measurements can be collected. In addition to the parameters estimated by an inverse problem, the governing mathematical models often involve simplifications, approximations, or modeling assumptions, resulting in additional  uncertainty. These additional uncertainties must be taken into account in the experimental design process; failing to do so could result in suboptimal designs. In this talk, we consider optimal design of infinite-dimensional Bayesian linear inverse problems governed by uncertain forward models. In particular, we seek experimental designs that minimize the posterior uncertainty in the primary parameters, while accounting for the uncertainty in secondary (nuisance) 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. 

References: This presentation is based on the following paper https://arxiv.org/abs/1308.4084 and manuscript https://arxiv.org/abs/2006.11939