Winter Semester 2015–2016: FU Berlin / BMS Course on Uncertainty Quantification
Lectures on the indicated days, 12:15–13:45 in SR E.31/A7, Arnimallee 7; exercises on the same day, 14:15–15:45 in SR 007/008, Arnimallee 6. See also the entries on the Course Catalogue here and here.
| Week | Date | Lecture Topic | Exercises | Notes / Comments |
|---|---|---|---|---|
| 1 | 15 Oct. 2015 | Introduction. Probability on function spaces. |  Exercise Sheet 1 |
Notes Chapters 1–5 |
| 2 | 22 Oct. 2015 | Hilbert spaces: direct sums and tensor products. | Exercise Sheet 2 |
Notes Backmatter |
| 3 | 29 Oct. 2015 | Convex, linear, and quadratic optimization. | Exercise Sheet 3 |
Proof of Theorem 4.19(d) has been corrected in the notes. |
| 4 | 5 Nov. 2015 | Information theory and distances between probability measures. | Exercise Sheet 4 |
N.B. Extended deadline for solutions. |
| 5 | 12 Nov. 2015 | Information theory, continued. Bayesian inverse problems. | (None) | Wrong factor of 2 in statement of Pinsker's inequality has been corrected in the notes; proof remains correct. |
| 6 | 19 Nov. 2015 | Data assimilation and filtering. | Exercise Sheet 6 |
|
| 7 | 26 Nov. 2015 | Bayesian inverse problems, continued. | (None) | |
| 8 | 3 Dec. 2015 | Orthogonal polynomials. | Exercise Sheet 8 |
|
| 9 | 10 Dec. 2015 | Orthogonal polynomials, continued. | ||
| 10 | 17 Dec. 2015 | Numerical integration. | ||
| 11 | 24 Dec. 2015 | No Classes (Christmas / New Year) | ||
| 12 | 31 Dec. 2015 | No Classes (Christmas / New Year) | ||
| 13 | 7 Jan. 2016 | Spectral expansions: the Karhunen–Loève theorem. | ||
| 14 | 14 Jan. 2016 | Wiener–Hermite and generalised polynomial chaos expansions. Intrusive (stochastic Galerkin) methods. | ||
| 15 | 21 Jan. 2016 | Intrusive (stochastic Galerkin) methods, continued. | ||
| 16 | 28 Jan. 2016 | Non-intrusive spectral projection methods. | ||
| 17 | 4 Feb. 2016 | Non-intrusive stochastic collocation methods. | ||
| 18 | 11 Feb. 2016 | Gaussian process interpolation and regression. | ||