Materials
The preliminary versions of the lecture slides can be found below. The slides may still be updated during the course.
Recommended supplementary reading: J. Kaipio and E. Somersalo, Statistical and Computational Inverse Problems, Springer, 2005 (mainly Chapters 2 and 3), and D. Calvetti and E. Somersalo, Introduction to Bayesian Scientific Computing. Ten Lectures on Subjective Computing, Springer, 2007.
February 24
Practical issues, motivation, compact operators and singular value decomposition, Fredholm equation and its solvability.
Lecture 1
lecture1.pdf129.3KB
February 28
Truncated singular value decomposition, pseudoinverse.
March 2
Morozov discrepancy principle, Tikhonov regularisation and its generalizations.
March 6
Regularization by truncated iterative methods: Landweber-Fridman iteration.
March 9
Regularization by truncated iterative methods: conjugate gradient method.
March 13
Conjugate gradient method (cont.), preliminaries of statistical inversion.
March 16
Preliminaries of statistical inversion (cont.), construction of likelihood.
March 20
Construction of likelihood (cont.), sampling, prior models.
https://aalto.cloud.panopto.eu/Panopto/Pages/Viewer.aspx?id=a707f988-7413-4f57-b107-ab8300b9da62
March 23
Prior models (cont.), n-variate Gaussian densities.
https://aalto.cloud.panopto.eu/Panopto/Pages/Viewer.aspx?id=91ab0e86-3047-4d5b-b4d8-ab84008885f2
March 27
Improper Gaussian priors, MCMC: Metropolis-Hastings algorithm.
https://aalto.cloud.panopto.eu/Panopto/Pages/Viewer.aspx?id=fcda6f1d-f094-4294-9fd5-ab8400c44951
March 30
Gibbs sampler, judging the quality of a sample.
https://aalto.cloud.panopto.eu/Panopto/Pages/Viewer.aspx?id=e0aad711-bdad-4e33-a030-ab8800c47b25
April 3
Hyper models.
https://aalto.cloud.panopto.eu/Panopto/Pages/Viewer.aspx?id=75430a96-aa39-4f50-b812-ab9100a53ebd