Research

Research Interests

My interests include statistics of inverse problems, Bayesian statistics, and stochastic analysis. Currently, I am working on Regression models driven by differential equations, where statistical theory meets the analysis of differential equations.

Preprints

• August 2023 - Sergio Brenner Miguel, Jan Johannes, Maximilian Siebel: Multiplicative deconvolution under unknown error distribution

Talks

• 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

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

Conferences

I was part of the organising committee of the 18. Doktorand:innentreffen der Stochastik in August 2023. I also attended the following conferences and workshops:

• 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 (>= 2 Weeks)

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

Theses

• 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