Research

  1. Publications
  2. Preprints
  3. Organised Conference Sessions
  4. (Upcoming) Talks
  5. Poster
  6. Conferences
  7. Research Stays
  8. Professional Activities
  9. Theses

Publications

Preprints

Organised Conference Sessions

  • Nordstat 2026 – 30th Nordic Conference in Mathematical Statistics, Helsinki, Jun 2026. Organiser of the contributed session Statistical guarantees for Bayesian inference in inverse problems.

(Upcoming) Talks

  • EMS 2026 – 35th European Meeting of Statisticians; Lugano, Switzerland; August 2026; Title: Parameter Estimation for Matérn Random Fields from Local Measurements.

  • Dynstoch 2026 - Statistical Methods for Dynamical Stochastic Models; Gothenburg, Sweden; June 2026; Title: “Posterior Contraction under Misspecification and Heteroscedasticity in Nonlinear Inverse Problems.”

  • Nordstat 2026 – 30th Nordic Conference in Mathematical Statistics; Helsinki, Finland; June 2026; Title: “Posterior Contraction under Misspecification and Heteroscedasticity in Nonlinear Inverse Problems.”

  • Research Seminar (Professor Markus Reiß), Humboldt-Universität zu Berlin, January 2026; Title: “Heteroscedasticity and mild misspecification in nonlinear statistical inverse problems.”

  • Research Seminar (Professor Claudia Schillings), Freie Universität Berlin, January 2026; Title: “Heteroscedasticity and mild misspecification in nonlinear statistical inverse problems.”

  • Scientific Computing Seminar (Professor Robert Scheichl), Heidelberg University, December 2025; Title: “Heteroscedasticity and mild misspecification in nonlinear statistical inverse problems.”

  • Conference: Stochastic partial differential equations: Statistics meets numerics; Institute Mittag-Leffler; Sweden; June 2025; Title: “Convergence Rates for the Maximum A Posteriori Estimator in PDE-Regression Models with Random Design”

  • GPSD 2025; Dresden, Germany; March 2025; Title: “Convergence Rates for the Maximum A Posteriori Estimator in PDE-Regression Models with Random Design”

  • Cosmology Discussion Seminar (Prof. Dr. Matthias Bartelmann); Heidelberg University; January 2025; Title: “Estimating Differential Equations in the presence of stochastic noise - A mathematical perspective”

  • Seminar AG Stochastik (Mathias Trabs); Karlsruhe Institute of Technology; November 2024; Title: “Convergence Rates for the Maximum A Posteriori Estimator in PDE-Regression Models with Random Design”

  • Workshop: Statistical Aspects of Non-Linear Inverse Problems; University of Cambridge, UK; September 17-19, 2024; Title: “Convergence Rates for the Maximum A Posteriori Estimator in PDE-Regression Models with Random Design”

  • Bernoulli-ims 11th World Congress in Probability and Statistics; Bochum, Germany; August 2024; Title: “Nonparametric Estimation of Ordinary Differential Equations”

  • Stochastics Seminar, Stochatsics Group, Aarhus University, May 2024; Title: “Multiplicative deconvolution under unknown error distribution”

  • Research Group Seminar, PIK FutureLab “AI in Anthropocene”, Potsdam, September 2023; Title: “Statistical Inference: Regression Models driven by Differential Equations”

  • Doktorrand:innentreffen Heidelberg - Mannheim, Mannheim, May 2023; Title: “Statistical Inverse Problems: PDE constrained Regression Models”

  • Applied Analysis Seminar, Heidelberg, June 2022; Title: “Statistical Inverse Problems: PDE constrained Regression Models”

Poster

  • Data-driven methods for partial differential equations, Karlsruhe, Germany, March 2026; Title: “Posterior contraction under misspecification and heteroskedasticity in non-linear inverse problems.”

  • YRC Structures Days, Heidelberg, July 2023; Title: “Statistical Inverse Problems: (P)DE Constrained Regression Models”

Conferences

I also attended the following conferences and workshops:

  • Dynstoch 2026 - Statistical Methods for Dynamical Stochastic Models; Gothenburg, Sweden; June 2026

  • Nordstat 2026 – 30th Nordic Conference in Mathematical Statistics; Helsinki, Finland; June 2026

  • Conference: Stochastic partial differential equations: Statistics meets numerics; Institute Mittag-Leffler; Sweden; June 2025

  • GPSD 2025; Dresden, Germany; March 2025

  • Workshop: Statistical Aspects of Non-Linear Inverse Problems; University of Cambridge, UK; September 2024

  • Bernoulli-ims 11th World Congress in Probability and Statistics; Bochum, Germany; August 2024

  • 11th Applied Inverse Problems Conference; Göttingen, Germany; September 2023

  • European Meeting of Statisticians; Warsaw, Poland; July 2023

  • Conference on statistical estimation; St. Etienne, France; June 2023

  • German Probability and Statistics Days 2023; Essen, Germany; March 2023

  • Workshop: Statistics for Stochastic Processes: SDEs, SPDEs and concentration of measure; University of Luxembourg; September 2022

  • 10th International Conference on Lévy Processes; Mannheim, Germany; July 2022

Research Stays

  • Research Group in Mathematical Statistics - Richard Nickl - University of Cambridge; April 2025 - July 2025

  • The Stochastics Group - Claudia Strauch - Aarhus University; May 2024

  • Potsdam-Institut für Klimafolgenforschung (PIK) - January 2024

  • Research Group in Mathematical Statistics - Richard Nickl - University of Cambridge; November 2023

Professional Activities

Theses

  • 2026 - PhD Thesis:

    This thesis investigates statistical methods for three classes of ill-posed inverse problems. In all models considered, observations arise as noisy versions of a transformed, yet unknown, target quantity. The objective is to develop estimation procedures for this quantity and to quantify their statistical accuracy within a rigorous mathematical framework. In the first part, we study statistical deconvolution problems in a multiplicative measure- ment error model, where both the density of the signal and that of the measurement errors are unknown. This setting leads to a linear inverse problem with an unknown operator. Based on spectral regularization techniques, we construct estimators and analyze their local and global risk. Furthermore, we develop a data-driven method for selecting the regularization parameter and derive upper bounds for the corresponding oracle-type risk. The second and third parts address regression models in which the regression functions are given by the solutions of ordinary or partial differential equations. The functions are evaluated at deterministic or random design points and observed under additive noise. The goal is to recover unknown parameters of the underlying differential equation. Due to the typically nonlinear nature of the solution operator, these models give rise to ill-posed nonlinear inverse problems. In the second part, we investigate both a penalized least squares approach and a Bayesian framework. In contrast to the existing literature, we analyze both methodologies under mild misspecification of model components such as the solution operator or the noise distribution. We establish consistency of the misspecified penalized least squares estimator and posterior contraction around the true parameter. The abstract results are applied to regression models governed by partial differential equations, with particular emphasis on the Darcy problem and the two-dimensional Navier-Stokes equations, where we derive upper bounds for both prediction and estimation errors. In the third part, we study the minimax optimality of such bounds. Concentrating on autonomous ordinary differential equations, we consider the problem of estimating the underlying vector field. After discussing suitable observation schemes to ensure identifiability, we derive lower bounds for the estimation error and establish the minimax optimality of existing procedures.

  • 2022 - Master Thesis:

    In this thesis, we are considering a non-parametric and non-linear regression problem, where the corresponding regression function is supposed to be the solution of an elliptic partial differential equation depending on an unknown coefficient function. Based on noisy versions of this solution, we want to recover the unknown coefficient function by defining a Least Squares estimator motivated by the theory of ill-posed linear statistical inverse problems. Afterward, we study the statistical quality of this estimator by deriving concentration inequalities and minimax optimal bounds. This approach is part of a more general model, which will be studied first. For a better understanding, we are further illustrating the statistical behavior of the estimator by numerical experiments.

    Literatur: Convergence rates for Penalised Least Squares Estimators in PDE-constrained regression problems; SIAM/ASA Journal on Uncertainty Quantification; Richard Nickl, Sara van de Geer, and Sven Wang

  • 2020 - Bachelor Thesis:

    In mathematical statistics, Bernstein-von Mises Theorems are regarded as the link between frequen- tistic statistics and the Bayesian approach, since under special conditions asymptotically equivalent results can be obtained. This thesis first introduces the different approaches of frequentistic statistics and of Bayesian statistics and motivates the consideration of Bernstein-von Mises Theorems in semi-parametric models. A generalised Bernstein-von-Mises Theorem is proved under the condition that the considered functional of interest satisfies certain regularity conditions. After specific adap- tions the generalised Theorem is applied to the White Noise Model and a corresponding Theorem is proved. Based on the theoretical foundations, the occurring effects of the Bernstein-von Mises Theorem are visualised in a slightly modified White Noise Model using a Monte-Carlo-Simulation and considering a linear functional of interest. The applicability of the Bernstein-von Mises Theorem is finally motivated in other statistical models, in particular in the Nonlinear Autoregressive Model and in the Density Model, respectively. Different mathematical principles used in this thesis are explained in detail at the beginning.

    Literatur: A Bernstein–von Mises theorem for smooth functionals in semiparametric models; Annals of Statistics; Ismaël Castillo, Judith Rousseau

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