Publications  Software  Talks  Teaching

Remo Kretschmann

Researcher in Mathematics

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ORCID: 0000-0002-4856-955X

About me

Most recently, I have been part of the research group Inverse Problems at the Chair of Mathematics IX at the Institute of Mathematics of the Julius-Maximilians-Universität Würzburg.

I have obtained my doctoral degree from the Universität Duisburg-Essen. My supervisor has been Prof. Christian Clason.

Before, I have studied mathematics at the Technische Universität München.

Research interests

• Statistical and Bayesian inverse problems with high- or infinite-dimensional parameter space, in particular the statistical properties of variational regularisation methods in the context of nonparametric Bayesian inference
• Inverse problems with non-Gaussian noise, impulsive noise models, imaging
• Uncertainty quantification, Gaussian approximation of the posterior distribution for high- or infinite-dimensional inverse problems
• Hypothesis testing for statistical inverse problems via regularisation or Bayesian inference

Experience

Education

Preprints

• Remo Kretschmann, Frank Werner:
  Maximum a posteriori testing in statistical inverse problems (pdf).

Publications

• Remo Kretschmann, Daniel Wachsmuth, Frank Werner:
  Optimal regularized hypothesis testing in statistical inverse problems (pdf)
  Inverse Problems 40 (2024), 015013.

• Remo Kretschmann:
  Are minimizers of the Onsager–Machlup functional strong posterior modes? (pdf)
  SIAM/ASA Journal on Uncertainty Quantification 11.4 (2023), 1105–1138.

• Tapio Helin, Remo Kretschmann:
  Non-asymptotic error estimates for the Laplace approximation in Bayesian inverse problems (pdf),
  Numerische Mathematik 150 (2022), 521–549.

• Dissertation:
  Nonparametric Bayesian Inverse Problems with Laplacian Noise (pdf),
  Fakultät für Mathematik, Universität Duisburg-Essen, 2019.

• 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.

• Master’s thesis (in German):
  Weak spectral synthesis on polynomial hypergroups (pdf),
  Department of Mathematics, Technische Universität München, 2012.

Software

• A direct sampler for probability distributions with density p(x) = exp(-a*x^2 - abs(b*x - c)), written in Octave (zip archive, 2.0 kB).

Recent talks

Conferences

• Bayesian hypothesis testing in statistical inverse problems,
  11th Applied Inverse Problems Conference, Göttingen, Germany, 4-8 September 2023.

• Bayesian hypothesis testing in statistical inverse problems,
  2nd HKSIAM Biennial Conference, Hong Kong, China, 28 August-1 September 2023.

• Optimal regularized hypothesis testing in statistical inverse problems,
  Computational Science and Engineering, Amsterdam, Netherlands, 27 February-3 March 2023.

• 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

• Optimal and Bayesian hypothesis testing in statistical inverse problems,
  Numerical analysis of stochastic and deterministic partial differential equations, Freie Universität Berlin, Germany, 28 November 2022.

• 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.

Teaching