Regularized hypothesis testing in Inverse Problems at work

• Applicant: Professor Dr. Frank Werner
• Subject Area: Mathematics
• Term: since 2021
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 466221855

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.

• DFG Programme: Research Grants