- Thesis:
- Bachelor in Mathematics
- Author:
- Merlin Dietrich
- Title:
- Deconvolution with an unknown kernel in a Bayesian perspective
- Supervisor:
- Jan JOHANNES
- Abstract:
- The aim of this thesis is to introduce the inverse problem of deconvolution with uncertainty in the operator in a Bayesian statistical setting. I will give a comprehensive formal introduction into Bayesian statistical modeling and keep the framework of the deconvolution as simple as possible, while still mapping the complexity of statistical inverse problems with unknown operators. I then present an approach of solving this inverse problem, that is entirely data driven, yet Bayesian. This ’solution’ will be justified in a rather frequentist analysis, by proving that it asymptotically concentrates around a postulated ’truth’. The idea of the data driven Bayesian ’solution’ and its analysis closely follow the lines of Trabs (2018) in his work on Bayesian inverse problems with unknown operators.
- References:
- M. Trabs. Bayesian inverse problems with unknown operators. Inverse Problems, 34(8):085001, 27, 2018.
| Statistics Group | Institute for Mathematics | Faculty of Mathematics and Computer Science | University Heidelberg |