DFG approves project on “Regularized hypothesis tests for inverse problems at work”
07/17/2025The German Research Foundation (DFG) is funding Professor Werner's project on “Regularized hypothesis testing for inverse problems at work” with around €250,000. This project aims to draw statistical conclusions about the properties of a noisy and indirectly observed variable, e.g., in the field of high-resolution microscopy.
Based on statistical hypothesis tests, the question of whether certain characteristics (such as the homogeneity of a function) are fulfilled can be answered with a given probability of error. In an earlier DFG project, a regulated approach to this problem was developed, but it still has various problems. On the one hand, two data samples are currently required to perform tests with a controlled type 1 error, and on the other hand, only individual characteristics can currently be tested. The overall goal of this project is to overcome these shortcomings of the regulated testing approach and to apply the developed methods using simulations and applications to real data, e.g., from high-resolution microscopy.
