- 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.