| Abstract: |
| One is often interested in estimating functional parameters in a partial differential equation given sparse and noisy observations of the solution. A Bayesian statistical methodology provides a comprehensive approach for such problems and establishing posterior consistency is an important step in validating this approach. In this talk I will introduce both posterior consistency and the Bayesian approach to inverse problems and present a newly developed abstract framework for establishing posterior consistency in PDE inverse problems. The abstract nature of the framework makes it easily adaptable to new problems unlike existing results which focus on specific problems. Additionally, and quite significantly, it allows for the use of fixed Gaussian priors and different observation types which are both absent in existing literature on PDE inverse problems. The talk should be readily accessible to anyone with a decent understanding of basic probability and PDE theory. This is joint work with Nathan Glatt-Holtz. |
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