After successful completion of the course, students are able to.describe the basic concepts of stochastic PDEs, their analysis, numerical solution and Bayesian techniques for various inverse
problems with applications in engineering, medicine and biology.

Introduction to PDE models with uncertainty, fundamentals of probability and random processes,
stochastic elliptic PDE models and applications, existence and uniqueness, stochastic numerical
methods, multilevel Monte-Carlo approximations, optimal multilevel methods, Bayesian inversion
techniques for parameter estimation, Markov-chain Monte-Carlo methods, well-posedness of
Bayesian estimation, optimal Bayesian experimental design, Bayesian analysis for semicon-
ductor devices (e.g., biosensors), electrical-impedance tomography in medical imaging and for
epidemiological models.

Lecture and presentation

Oral exam