Project Leader: Prof. Frank Werner, Professorship Inverse Problems at the Chair of Mathematics IX (Chair Scientific Computing), University of Würzburg, Germany.
Project period: 10.2021 - 09.2023
Funding institution: DFG
Funding amount: 200.000,00 €
Granting date: 11.06.2021
Funding number: WE 6204/2-1
This project aims to statistically infer on properties of a noisy and indirectly observed quantity of interest. Based on statistical hypothesis testing, the question whether specific features (such as homogeneity of a function) are satisfied can be answered with a prescribed error probability. The problem is therefore studied in a classical inverse problems setup, and regularized hypothesis tests based on optimal estimators are studied. Besides theoretical considerations, this project also aims to study the developed methods by means of simulations and applications to real world data, e.g. from super-resolution microscopy.