Regularized hypothesis testing in statistical inverse problems

• 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. 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.

• DFG Programme: Research Grants