Björn Sprungk | TU Bergakademie Freiberg | Germany
The computational efficiency of many common sampling methods for Bayesian inverse problems suffers from a large state space dimension, a costly likelihood function, and a concentrated posterior measure. Concerning the first two issues, several modifications of classical algorithms have been proposed and studied during the last few years, such as multilevel Monte Carlo methods or Metropolis-Hastings algorithms in infinite-dimensional spaces. In this talk we discuss how the challenge of sampling from concentrated posteriors can be tackled. To this end, we exploit the Laplace approximation of the posterior in order to inform the sampling method about its concentration. In particular, we study a generalization of the dimension-independent pCN-Metropolis algorithm which uses the covariance of the Laplace approximation. The resulting algorithm shows a provably robust performance with respect to the concentration of the posterior as well as the dimension of the state space. Moreover, we study importance sampling based on the Laplace approximation and show that it becomes more efficient as the posterior concentrates.