Reports:

• Please hand in the reports before the 31st of March 2024.
• The report should be roughly six pages long.

Topics:

1. Design of experiments for X-ray tomography
   Two topics available:
   - Paper 1: https://arxiv.org/abs/2006.12579
   - Paper 2: https://arxiv.org/abs/2104.00301

2. Bayesian inversion using alpha-stable priors
   - Paper: https://doi.org/10.1088/1361-6420/acf154

3. Analytic and Gevrey class regularity for PDE uncertainty quantification
   - Paper: https://arxiv.org/pdf/2309.17397.pdf
   Note that this topic can be divided into a theoretical part and a numerical part, which can be studied separately.

4. Well-posedness of Bayesian inverse problems:

   https://ui.adsabs.harvard.edu/abs/2019arXiv190210257L/abstract

5. (Bayesian) Probabilistic numerical methods

   main paper: https://epubs.siam.org/doi/10.1137/17M1139357

   additional: https://projecteuclid.org/journals/bayesian-analysis/volume-14/issue-3/A-Bayesian-Conjugate-Gradient-Method-with-Discussion/10.1214/19-BA1145.full

6. Kernel Stein Discrepancy and Stein Variational Gradient Descent

   https://proceedings.mlr.press/v48/liub16.html

   https://proceedings.mlr.press/v48/chwialkowski16.html

   https://proceedings.neurips.cc/paper_files/paper/2016/hash/b3ba8f1bee1238a2f37603d90b58898d-Abstract.html

7. Diffusion models (taken by Charlotte, literature will come soon)

8. Particle methods for design of experiment https://www.tandfonline.com/doi/pdf/10.1198/016214505000001159
9. Bayesian optimization with discrete variables https://arxiv.org/pdf/2210.10199.pdf
10. Bayesian optimization in high dimensions https://ml.informatik.uni-freiburg.de/wp-content/uploads/papers/13-IJCAI-BO-highdim.pdf