Activites and Courses

The forthcoming activities of the research project – summer schools, workshops, training sessions, etc. – will be announced here.

PhD course: Bayesian Scientific Computing

Bayesian statistics is concerned with inference on variables that are not directly observable, the unknowns of primary interest, based a priori information about them plus observation of other quantities that depend indirectly on the variables of interest. The connection between Bayesian inference and inverse problems, the science of estimating variables from noisy indirect measurements is clear, and presently Bayesian methods in inverse problems are widely used. The interplay between ideas from scientific computing for inverse problems and Bayesian methods for inference gives rise to Bayesian scientific computing, which the topic of this course.

The lectured will focus on basic techniques in Bayesian methods, including probability distributions, Bayes' formula, conditioning, hierarchical models, estimation problems arising in this context, as well as certain numerical techniques for inverse problems, including regularization and iterative methods for solving large systems. In the lectures the connections between computational inverse problems and Bayesian inference will be highlighted. The Bayesian methods developed in the course will be used to solve inverse problems with sparsity constraints and dynamically update estimates with classical filtering techniques such as Kalman filtering.

The course consists of lectures and MATLAB based exercises, and is based on the book: D.  Calvetti and E. Somersalo, Introduction to Bayesian Scientific Computing, Springer, 2007, as well as a preliminary new edition of it.

Ects: 2.5.
Time: December 9-13, 2019 (one full week).
Teacher: Professor Daniela Calvetti and Professor Erkki Somersalo, both from Case Western Reserve University, Ohio.
Course responsible, contact: Professor Per Christian Hansen, DTU.
More details: course description in progress.

PhD course: Computational Uncertainty Quantification for Inverse Problems

Uncertainty Quantification (UQ) is the science of quantifying, characterizing, tracing, and managing uncertainty in computational and real world systems. This course is aimed at PhD students and researchers in applied mathematics and physics who want to understand and use UQ in connection with inverse problems such as image deblurring, computed tomography, and inverse scattering.

The course consists of lectures and exercises using MATLAB. The topics are: a review of computational inverse problems, Bayesian methods and UQ for inverse problems, prior modeling with Markov random fields, and recently developed MCMC methods for UQ in inverse problems. The course ends with a mini-project done by the course participants.

The course uses the book: J. M. Bardsley, Computational Methods and Uncertainty Quantification for Inverse Problems, SIAM, 2018.

Ects: 2.5.
Time: one week in May 2020 (the dates are not settled yet).
Teacher: Professor Johnathan M. Bardsley, University of Montana.
Course responsible, contact: Professor Per Christian Hansen, DTU.
More details: see course description.