My name is Jonas Latz. I am currently a mathematics PhD student in the group of Elisabeth Ullmann at the Technical University of Munich (TUM). Our research is at the interface of numerical analysis, computational science, probability theory, and statistics. It focuses on methods that can be used to blend mathematical models with observational data.
|Uncertainty quantification||Bayesian inference||Inverse problems|
|Well-posedness||Measures and integration||Markov chain Monte Carlo|
|Particle filters||Real world data||Low-rank approximation|
|Multilevel methods||Hierarchical models||(Stochastic) partial differential equations|
This webpage contains information about my research output in academic journals and at academic meetings. Moreover, I have summarised my teaching experience and my personal background. Input of any kind is highly appreciated; please contact me.
My colleague Björn Sprungk (Göttingen) and I had submitted a minisymposium to the SIAM Conference on Uncertainty Quantification, which will take place in the end of March 2020 in Munich, Germany. Our minisymposium has now been approved by the conference’s scientific committee. Its title reads “Would Hadamard have used Bayes’ rule? - On robustness and brittleness of statistical inversion”. We are looking forward to four very interesting talks, which are going to cover: stability and instability of Bayesian inference subject to perturbations in data, model, or prior; consistency subject to large data limits and convergence of Gaussian process surrogates/emulators; and influences of perturbations in MCMC algorithms.
Fabian Wagner, Iason Papaioannou, Elisabeth Ullmann and I have deposited a new manuscript in the arXiv: “Multilevel Sequential Importance Sampling for Rare Event Estimation”. In this manuscript, we essentially work towards employing the Multilevel Sequential² Monte Carlo framework for the estimation of rare events rather than Bayesian inversion; see (2018, J. Comput. Phys. 368, p. 154-178). Then, we show in numerical experiments that this approach is reasonable and that it can outperform single level strategies. Moreover, the approach solves nestedness issues that can occur in Subset Simulation algorithms. Last, I want to mention that we consider MCMC algorithms that are based on adaptive von Mises-Fischer-Nakagami proposals. Those appear to be especially useful in the mutation step in Sequential Monte Carlo methods. For more information, please have a look at the article.
As of tonight, a new version of the manuscript “On the well-posedness of Bayesian inverse problems” is available in the arXiv. Aside from a slight change of the paper’s focus, I have added some new results concerning stability in the Wasserstein distance and considered the case of infinite-dimensional data spaces with additive Gaussian noise. The latter complements the results we have already had for finite-dimensional noise – here, we could already show well-posedness independently of prior and forward model. Additionally, the infinite-dimensional case gives a new connection between this manuscript and the recent article of Christian Kahle, Kei Fong Lam, Elisabeth Ullmann, and me; see (2019, SIAM/ASA J. Uncertain. Quantif. 7(2), p. 526-552).
I have a new academic webpage and you found it! Please feel free to take a stroll around the side.