Research
Research Interests
- Nonparametric and high-dimensional statistics
- Statistics for stochastic processes
- Statistical inverse problems
- Statistical learning
- Stochastic (partial) differential equations
Current Projects
DASHH is a Helmholtz graduate school involving several partner institutions in Hamburg. In DASHH we harness data, computer and applied mathematical science to advance our understanding of nature. We aim to educate the future generation of data- and information- scientists that will tackle tomorrow's scientific challenges that come along with large-scale experiments.
Past Projects
- DFG project TR1349/3-1 "High-dimensional statistics for point and jump processes", GEPRIS (2019 - 2023)
- LD-SODA: Learning-based data analysis - stochastics, optimization, dynamics and approximation (Landesforschungsförderung Hamburg)
Current and past PhD students:
| 2026 - now | Andreas Hillebrand | Heidelberg University | |
| 2025 - now | Philippe Arts | Joint supervision with Ralf Loritz | Karlsruhe Institute of Technology |
| 2025 - now | Christoph Müller | Karlsruhe Institute of Technology | |
| 2022 - 2025 | Lea Kunkel | Statistical Guarantees for Generative Models as Distribution Estimators | Karlsruhe Institute of Technology |
| 2021 - 2026 | Thea Engler | Illumination Correction in X-Ray Near-Field Holography: From Dynamic Intensities to Full Wave Fields (Joint supervision with Christian Schroer and Johannes Hagemann) | Desy |
| 2021 - 2025 | Jan Rabe | Asymptotic confidence bands for centered purely random forests (Joint supervision with Natalie Neumeyer) | University of Hamburg |
| 2021 - 2024 | Sebasian Bieringer | Uncertainties in Generative Deep Learning and Data Amplification for High Energy Physics (joint supervision with Gregor Kasieczka) | University of Hamburg |
| 2019 - 2024 | Maximilian F. Steffen | Multivariate estimation in nonparametric models: Stochastic neural networks and Lévy processes | Karlsruhe Institute of Technology |
| 2017 - 2021 | Florian Hildebrandt | Parameter estimation for SPDEs based on discrete observations in time and space | University of Hamburg |
Short CV
| Since 2021 | Professor at Karlsruhe Institute of Technology |
| 2021 | Heisenberg professor at University of Hamburg |
| 2016 - 2021 | Assistant professor at University of Hamburg |
| 2015 - 2016 | DFG research fellow at Université Paris-Dauphine |
| 2014 - 2015 | Postdoctoral researcher at Humboldt-Universität zu Berlin |
| 2014 | Visiting Ph.D. student at the University of Cambridge, UK |
| 2011 - 2014 | Ph.D. study in Mathematics at Humboldt-Universität zu Berlin |
| 2007 - 2011 | Studies in Mathematics with minor Economics at Humboldt-Universität zu Berlin |
Preprints
- Statistical inference for the stochastic wave equation based on discrete observations with Anton Tiepner and Eric Ziebell, arXiv: 2602.04708
- Asymptotic confidence bands for centered purely random forests with Natalie Neumeyer and Jan Rabe, arXiv: 2511.13199
- Asymptotic confidence bands for the histogram regression estimator with Natalie Neumeyer and Jan Rabe, arXiv: 2508.12391
- On the minimax optimality of Flow Matching through the connection to kernel density estimation with Lea Kunkel, arXiv: 2504.13336
- AdamMCMC: Combining Metropolis Adjusted Langevin with Momentum-based Optimization with Sebastian Bieringer, Gregor Kasieczka and Maximilian F. Steffen, arXiv: 2312.14027
Books
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Trabs, M.; Jirak, M.; Krenz, K.; Reiß, M.
Statistik und maschinelles Lernen – Eine mathematische Einführung in klassische und moderne Methoden
2021. Springer-Verlag. doi:10.1007/978-3-662-62938-3
Publications
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Bieringer, S.; Kasieczka, G.; Steffen, M. F.; Trabs, M.
The surrogate Gibbs-posterior of a corrected stochastic MALA: Towards uncertainty quantification for neural networks
2026. Journal of Machine Learning Research, 27 (1), 1–50 -
Steffen, M. F.; Trabs, M.
A PAC-Bayes Oracle Inequality for Sparse Neural Networks
2026. Applications of Mathematics in Sciences, Engineering, and Economics – MathSEE Symposium, Karlsruhe, September 27–29, 2023. Ed.: A. Ott, 131–151, Springer Nature Switzerland. doi:10.1007/978-3-032-01279-1_7 -
Nikolaev, P.; Prömel, D. J.; Trabs, M.
Characterization of Besov spaces with dominating mixed smoothness by differences
2025. Mathematische Nachrichten, 298 (7), 2116–2151. doi:10.1002/mana.202400122 -
Ehrenreich-Petersen, E.; Massani, B.; Engler, T.; Pardo, O. S.; Glazyrin, K.; Giordano, N.; Hagemann, J.; Sneed, D.; Fedotenko, T.; Campbell, D. J.; Wendt, M.; Wenz, S.; Schroer, C. G.; Trabs, M.; McWilliams, R. S.; Liermann, H.-P.; Jenei, Z.; O’Bannon, E. F.
X-ray phase contrast imaging and diffraction in the laser-heated diamond anvil cell: A case study on the high-pressure melting of Pt
2025. Results in Physics, 69, Art.-Nr.: 108132. doi:10.1016/j.rinp.2025.108132 -
Kunkel, L.; Trabs, M.
A Wasserstein perspective of Vanilla GANs
2025. Neural Networks, 181, 106770. doi:10.1016/j.neunet.2024.106770 -
Bieringer, S.; Diefenbacher, S.; Kasieczka, G.; Trabs, M.
Calibrating Bayesian generative machine learning for Bayesiamplification
2024. Machine Learning: Science and Technology, 5 (4), Art.-Nr.: 045044. doi:10.1088/2632-2153/ad9136 -
Bieringer, S.; Kasieczka, G.; Kieseler, J.; Trabs, M.
Classifier surrogates: sharing AI-based searches with the world
2024. The European Physical Journal C, 84 (9), Art.-Nr.: 972. doi:10.1140/epjc/s10052-024-13353-w -
Hildebrandt, F.; Trabs, M.
Nonparametric calibration for stochastic reaction–diffusion equations based on discrete observations
2023. Stochastic Processes and their Applications, 162, 171–217. doi:10.1016/j.spa.2023.04.019 -
Hoffmann, M.; Trabs, M.
Dispersal density estimation across scales
2023. The Annals of Statistics, 51 (3), 1258–1281. doi:10.1214/23-AOS2290 -
Eckstein, S.; Iske, A.; Trabs, M.
Dimensionality Reduction and Wasserstein Stability for Kernel Regression
2023. Journal of Machine Learning Research, 24 -
Bieringer, S.; Butter, A.; Diefenbacher, S.; Eren, E.; Gaede, F.; Hundhausen, D.; Kasieczka, G.; Nachman, B.; Plehn, T.; Trabs, M.
Calomplification — the power of generative calorimeter models
2022. Journal of Instrumentation, 17 (09), Art.Nr. P09028. doi:10.1088/1748-0221/17/09/P09028 -
Prömel, D. J.; Trabs, M.
Paracontrolled distribution approach to stochastic Volterra equations
2021. Journal of Differential Equations, 302, 222–272. doi:10.1016/j.jde.2021.08.031 -
Hildebrandt, F.; Trabs, M.
Parameter estimation for SPDEs based on discrete observations in time and space
2021. Electronic Journal of Statistics, 15 (1), 2716–2776. doi:10.1214/21-EJS1848 -
Trabs, N.; Trabs, M.; Stodieck, S.; House, P. M.
Influence of stiripentol on perampanel serum levels
2020. Epilepsy Research, 164, Article no: 106367. doi:10.1016/j.eplepsyres.2020.106367 -
Bibinger, M.; Trabs, M.
Volatility estimation for stochastic PDEs using high-frequency observations
2020. Stochastic Processes and their Applications, 130 (5), 3005–3052. doi:10.1016/j.spa.2019.09.002 -
Belomestny, D.; Trabs, M.; Tsybakov, A. B.
Sparse covariance matrix estimation in high-dimensional deconvolution
2019. Bernoulli, 25 (3). doi:10.3150/18-BEJ1040A -
Niebuhr, T.; Trabs, M.
Profiting from correlations: Adjusted estimators for categorical data
2019. Applied Stochastic Models in Business and Industry, 35 (4), 1090–1102. doi:10.1002/asmb.2452 -
Bibinger, M.; Trabs, M.
On Central Limit Theorems for Power Variations of the Solution to the Stochastic Heat Equation
2019. Stochastic Models, Statistics and Their Applications – Dresden, Germany, March 2019. Ed.: A. Steland, 69–84, Springer International Publishing. doi:10.1007/978-3-030-28665-1_5 -
Belomestny, D.; Trabs, M.
Low-rank diffusion matrix estimation for high-dimensional time-changed Lévy processes
2018. Annales de l’Institut Henri Poincaré, Probabilités et Statistiques, 54 (3), 1584–1621. doi:10.1214/17-AIHP849 -
Trabs, M.
Bayesian inverse problems with unknown operators
2018. Inverse Problems, 34 (8), Article no: 085001. doi:10.1088/1361-6420/aac3aa -
Chorowski, J.; Trabs, M.
Spectral estimation for diffusions with random sampling times
2016. Stochastic Processes and their Applications, 126 (10), 2976–3008. doi:10.1016/j.spa.2016.03.009 -
Prömel, D. J.; Trabs, M.
Rough differential equations driven by signals in Besov spaces
2016. Journal of Differential Equations, 260 (6), 5202–5249. doi:10.1016/j.jde.2015.12.012 -
Nickl, R.; Reiß, M.; Söhl, J.; Trabs, M.
High-frequency Donsker theorems for Lévy measures
2016. Probability Theory and Related Fields, 164 (1-2), 61–108. doi:10.1007/s00440-014-0607-3 -
Dattner, I.; Reiß, M.; Trabs, M.
Adaptive quantile estimation in deconvolution with unknown error distribution
2016. Bernoulli, 22 (1). doi:10.3150/14-BEJ626 -
Söhl, J.; Trabs, M.
Adaptive confidence bands for Markov chains and diffusions: Estimating the invariant measure and the drift
2016. ESAIM: Probability and Statistics, 20, 432–462. doi:10.1051/ps/2016017 -
Trabs, M.
Information bounds for inverse problems with application to deconvolution and Lévy models
2015. Annales de l’Institut Henri Poincaré, Probabilités et Statistiques, 51 (4), 1620–1650. doi:10.1214/14-AIHP627 -
Trabs, M.
Quantile estimation for Lévy measures
2015. Stochastic Processes and their Applications, 125 (9), 3484–3521. doi:10.1016/j.spa.2015.04.004 -
Söhl, J.; Trabs, M.
Option calibration of exponential Lévy models: confidence intervals and empirical results
2014. The Journal of Computational Finance, 18 (2), 91–119. doi:10.21314/JCF.2014.275 -
Trabs, M.
On infinitely divisible distributions with polynomially decaying characteristic functions
2014. Statistics & Probability Letters, 94, 56–62. doi:10.1016/j.spl.2014.07.002 -
Trabs, M.
Calibration of self-decomposable Lévy models
2014. Bernoulli, 20 (1). doi:10.3150/12-BEJ478 -
Söhl, J.; Trabs, M.
A uniform central limit theorem and efficiency for deconvolution estimators
2012. Electronic Journal of Statistics, 6, 2486–2518. doi:10.1214/12-EJS757
Further activities
- Deputy speaker of the KIT Center MathSEE Mathematics in Sciences, Engineering, and Economics
- Member of the steering board of the DMV-Fachgruppe Stochastik (Probability and Statistics Group of the German Mathematical Society)
- Member of the steering board of the KIT Graduate School Computational and Data Science (KCDS)
- Associate editor for Statistics
- Associate editor for ESAIM: Probability and Statistics