Seminar in Numerical Analysis: Björn Sprungk (TU Freiberg)

Sampling methods for Bayesian inverse problems

In this talk we consider the Bayesian approach to inverse problems which allows for uncertainty quantification for the data-driven reconstruction of the ground truth. After a brief dicussion of the well-posedness and local Lipschitz stability of Bayesian inverse problems, we focus on Markov chain Monte Carlo methods for sampling and integration with respect to the posterior probability distribution. Here we present our contributions to Metropolis-Hastings algorithms in function spaces, discuss convergence in terms of geometric ergodicity and present numerical experiments which show a dimension-indepedent performance which is, moreover, robust to the level of observational noise in the data. In the last part of the talk we present recent results of combining Metropolis-Hastings with interacting particle sampling methods based on Euler-Maruyama discretizations of stochastic differential equations of McKean-Vlasov type.

For further information about the seminar, please visit this webpage.

Veranstaltung übernehmen als iCal