Projects
Project Leader: Prof. Frank Werner, Professorship Inverse Problems at the Chair of Mathematics IX (Chair Scientific Computing), University of Würzburg, Germany.
Project period: 2025 - 2028
Funding institution: DFG
Funding amount: 250.000,00 €
Granting date: 11.06.2025
Funding number: WE 6204/2-3
Project Description:
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. In a previous DFG project, a regularized approach to this problem has been established, which albeit still suffers from different issues. On the one hand, two samples of data are currently required to perform testing with a controlled type 1 error, and on the other hand, only single features can be tested at the moment. The overall aim of the project at hand is to overcome these shortcomings of the regularized testing approach, and to apply the developed methods by means of simulations and applications to real world data, e.g. from super-resolution microscopy.
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
Project Description:
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.
