Abstract

In the second talk, I want to discuss some practical aspects of Bayesian inference applied to inverse problems. As an exemplary application, I will consider solving high-dimensional inverse problems using sparsity constraints as a-priori information, e.g., the well-known total variation (TV) minimization constraint. After explaining the basic principles and algorithms of Markov chain Monte Carlo (MCMC) based posterior inference, I will show that contrary to what is commonly believed about the applicability of MCMC schemes, they are not in general slow and scale bad with increasing dimension. In addition, I will outline why I think that designing efficient optimization and sampling techniques is conceptually similar, and highlight some recent work on enhancing sampling by incorporating ideas from optimization.

Slides of this talk can be downloaded at http://wwwmath.uni-muenster.de/num/burger/organization/lucka/talks/Cambridge2_14_11_2012.pdf