Projects
Project Leader: Prof. Dr. Frank Werner, Professur Inverse Probleme am Lehrstuhl für Mathematik IX (Chair Scientific Computing), University of Würzburg, and PD Dr. med. Dirk Weismann, Medical Clinic and Polyclinic I of the University Medical Center Internal Medicine (ZIM)
Project period: 2026
Funding institution: Vogel Stiftung Dr. Eckernkamp
Funding amount: 11.000,00 €
Granting date: 12.12.2025
Project Description:
Randomized clinical trials are the medical gold standard for independent and unbiased assessment of interventions. At the same time, large amounts of data are collected from intensive care patients in internal emergency and intensive care medicine. From a mathematical perspective, these data represent different time series for each intensive care patient, each corresponding to a measurement parameter. We base our hypothesis on the assumption that this data can be understood as autoregressive with a moving average, which raises the question of regularities that could also be used for randomization, for example.
In this project, we want to start by analyzing the existing data using classic methods of statistics and data science such as clustering, UMAP, and PCA. In a second step, once we have a basic understanding, we plan to apply more complex mathematical methods and models, e.g., from time series analysis or deep learning.
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.
