Topic outline

  • 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.

    • Fedruary 25

      Practical issues, motivation, compact operators and singular value decomposition, Fredholm equation and its solvability. 

    • March 1

      Truncated singular value decomposition, pseudoinverse.

    • March 4

      Morozov discrepancy principle, Tikhonov regularisation and its generalizations.

    • March 8

      Regularization by truncated iterative methods: Landweber-Fridman iteration.

    • March 11

      Regularization by truncated iterative methods: conjugate gradient method.

    • March 15

      Conjugate gradient method (cont.), preliminaries of statistical inversion.

    • March 18

      Preliminaries of statistical inversion (cont.), construction of likelihood.

    • March 22

      Construction of likelihood (cont.), sampling, prior models.

    • March 25

      Prior models (cont.), n-variate Gaussian densities.

    • March 29

      Improper Gaussian priors, MCMC: Metropolis-Hastings algorithm.

    • April 1

      Gibbs sampler, judging the quality of a sample.

    • April 5

      Hyper models.

Next section ►
Assignments