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Statistical Inverse Problems and PDEs: Progress and Challenges
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- 1 Intro
- 2 Lecture Notes
- 3 Statistical inverse regression models
- 4 Inverse problems and partial differential equations (PDES)
- 5 PDE model examples
- 6 Illustration for neutron tomography
- 7 Challenges for inversion
- 8 Bayesian Inverse Problems (Stuart (2010))
- 9 Computation: gradient based MCMC
- 10 Bayesian inversion with Gaussian process priors in action
- 11 Illustration of MCMC
- 12 Mathematical guarantees for such algorithms?
- 13 Algorithmic guarantees I: Posterior consistency with GPS
- 14 Algorithmic guarantees II: Computation in high-dimensions
- 15 Proof ideas
- 16 Hardness of cold-start MCMC
- 17 Conclusions
