Research Assistant
Dr. Remo Kretschmann

Research Interests
My research interests are, i.a., statistical and Bayesian inverse problems with high- or infinite-dimensional parameter space and regularisation theory, in particular the rigorous statistical interpretation of variational regularisation methods in the context of nonparametric Bayesian inference.
Education
August 2019 | Doctorate in Mathematics, Universität Duisburg-Essen |
November 2012 | Master of Science in Mathematics, Technische Universität München |
November 2009 | Bachelor of Science in Mathematics, Technische Universität München |
Preprints
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Remo Kretschmann, Daniel Wachsmuth, Frank Werner:
Optimal regularized hypothesis testing in statistical inverse problems
(2022), arXiv: 2212.12897 (pdf). -
Remo Kretschmann:
Minimizers of the Onsager-Machlup functional are strong posterior modes
(2022), arXiv: 2212.04275 (pdf).
Refereed Articles
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Tapio Helin, Remo Kretschmann:
Non-asymptotic error estimates for the Laplace approximation in Bayesian inverse problems (pdf),
Numerische Mathematik 150, 521–549 (2022). -
Christian Clason, Tapio Helin, Remo Kretschmann, Petteri Piiroinen:
Generalized modes in Bayesian inverse problems (pdf),
SIAM/ASA Journal on Uncertainty Quantification 7.2 (2019), 652–684.
Theses
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Nonparametric Bayesian Inverse Problems with Laplacian Noise (pdf),
Fakultät für Mathematik, Universität Duisburg-Essen, 2019.
Conferences
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Bayesian hypothesis testing in statistical inverse problems,
Imaging with Uncertainty Quantification, Helsingør, Denmark, 27-29 September 2022. -
Optimal regularized hypothesis testing in statistical inverse problems,
Symposium on Inverse Problems: From experimental data to models and back, Universität Potsdam, Potsdam, Germany, 19-21 September 2022. -
Non-asymptotic error estimates for the Laplace approximation in Bayesian inverse problems,
13th International Conference on Monte Carlo Methods and Applications, Universität Mannheim, online, 16-20 August 2021. -
Non-asymptotic error estimates for the Laplace approximation in Bayesian inverse problems,
Inverse Days 2020, Finnish Meteorological Institute/University of Helsinki, online, 14-18 December 2020. -
Generalised modes in Bayesian inverse problems,
25th Inverse Days, University of Jyväskylä, Jyväskylä, Finland, 16-18 December 2019. -
Generalized modes in Bayesian inverse problems (poster presentation),
12th International Conference on Bayesian Nonparametrics, University of Oxford, Oxford, United Kingdom, 24-28 June 2019. -
Generalized modes in Bayesian inverse problems,
Chemnitz Symposium on Inverse Problems 2018, Technische Universität Chemnitz, Chemnitz, Germany, 27-28 September 2018. -
Bayesian inverse problems with non-Gaussian noise (poster presentation),
38th International Workshop on Bayesian Inference and Maximum Entropy Methods in Science and Engineering, The Alan Turing Institute, London, United Kingdom, 02-06 July 2018. -
Bayesian inverse problems with Laplacian noise,
Applied Inverse Problems 2017, Zhejiang University, Hangzhou, China, 29 May-2 June 2017.
Seminars
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Generalised modes in Bayesian inverse problems,
University of Helsinki, Helsinki, Finland, 9 December 2019. -
Bayesian inverse problems with Laplacian noise,
University of Graz, Graz, Austria, 28 September 2017.
2021 | Course on Bayesian inverse problems |
2020 | Intensive course on Bayesian inverse problems |
2018 | Master seminar on Inverse problems |
2017–2018 | Tutorial on Inverse problems |
2017 | Tutorial on Analysis I |
2016–2017 | Tutorials on Regularisation of Inverse problems and Analysis II |
2016 | Tutorial on Iterative methods for systems of linear equations and eigenvalue problems |
2015–2016 | Tutorial on Inverse problems |
2015 | Tutorial on Functional analysis |
2014–2015 | Tutorial on Inverse problems |
2014 | Tutorial on Scientific computing for differential equations |
2011 | Tutorials on Analysis I and Higher mathematics for civil engineers 2 |