Projects

My research has three goals:

  • Stochastics is the basis for understanding in the life sciences. Fields of application that we work on are population genetics, forensic genetics and neuroscience.
  • The characterization and convergence of stochastic processes can be studied by (so-called) martingale problems. We are working on the development of new convergence results using this technique.
  • In recent years, mathematicians can formalize their research results using the Lean Theorem prover. We are working to expand the stochastics section of the corresponding library.

We consider $K$ populations and data on the DNA sequence at $M$ different positions (i.e., we use $M$ different markers) for $N$ individuals. Based on this knowledge, we estimate the ancestry of individuals with the Admixture Model. Specifically, we assume that the ancestry of each individual is a mixture of the $K$ non-admixed populations, such as those from Europe or Africa.

We mainly focus on the following topics concerning the ancestry of individuals:

  • Theoretical Properties of the Estimator: The ancestry is often estimated with a Maximum-Likelihood Estimator. We prove some theoretical properties of this estimator, e.g. consistency and central limit results. Marker Selection: The question arises which markers are the best ones for the estimation of the ancestry. We use central limit results to answer this question.
  • Classification: In the forensic genetics, researchers often classify the individuals into populations. The output is the probability that an individual comes from a specific population. We combine – together with Frank Hutter and Lennart Purucker – machine learning and probability theory to improve the state-of-the-art method to classify individuals into populations.
  • Statistical Test: It might be that the parents of an individual are from different populations. Then, it does not make sense to classify this individual into one single population. We provide statistical tests to e.g. evaluate whether the classification makes sense. A Part of this work is joint with Sabine Lutz-Bonengel.
Zusammen mit Angelika Rohde und Sabine Lutz-Bonengel bin ich Projektleiter in einem Projekt zur forensischen Genetik des Sonderforschungsbereichs Small Data.

TEs

CRNs

Lean