Tim Sullivan

Junior Professor in Applied Mathematics:
Risk and Uncertainty Quantification

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. PDF Exercise Sheet 1 PDF Notes Chapters 1–5
2 22 Oct. 2015 Hilbert spaces: direct sums and tensor products. PDF Exercise Sheet 2 PDF Notes Backmatter
3 29 Oct. 2015 Convex, linear, and quadratic optimization. PDF 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. PDF 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. PDF Exercise Sheet 6  
7 26 Nov. 2015 Bayesian inverse problems, continued. (None)  
8 3 Dec. 2015 Orthogonal polynomials. PDF 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.