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职业迁徙
个人简介
My research is directed to statistical inference for stochastic processes, with focus on uncertainty quantification and indirect observation schemes. I work on Bayesian computational aspects of inference for discretely observed stochastic processes on graphical models with particular emphasis on diffusion- and Lévy processes. Within Bayesian estimation for diffusions, the simulation of diffusion bridges is of key importance. Together with Moritz Schauer (University of Gothenburg) I have developed general methods for simulating conditioned Markov processes using an algorithm called backward filtering forward guiding. One exciting application of the developed methods is shape deformation (ongoing cooperation with Stefan Sommer (University of Copenhagen) and Alexis Arnaudon (Ecole Polytechnique Federale de Lausanne)). For implementation of landmark matching and template estimation, see BridgeLandmarks. Related to this topic, Marc Corstanje works in his phd-project on inference methods for diffusions on manifolds. Thorben Pieper works on inference for stochastic partial differential equations.
Together with Shota Gugushvili (Wageningen University), Peter Spreij (University of Amsterdam) and Moritz Schauer I have considered various problems of nonparametric function estimation, where it is assumed that the function is piecewise constant, but adjacent bins are coupled such that the values of these have positive dependence. This appears to work well in a wide range of settings and we may expand this work to other settings or possibly work on stronger theoretical validation of this approach.
More generally, I am interested in Bayesian computational methods such as Markov Chain Monte Carlo (MCMC) and Sequential Monte Carlo (SMC). Recently I have also worked on piecewise deterministic processes such as the (sticky) ZigZag process (with Sebastiano Grazzi and Joris Bierkens). On a somewhat more theoretical level I am interested in proving posterior contraction rates for Bayesian procedures, for example in censoring or shape restricted nonparametric problems. Finally an important aspect of my research consists of direct collaboration with researchers in fields outside mathematics. Examples include sports engineering (with Larisa Gomaz, analysis of multilevel longitudinal data), climate projections (with Lörinc Mészáros) and maritime engineering (fatigue calculations of maritime structures).
研究兴趣
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arxiv(2024)
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arXiv (Cornell University) (2023)
arxiv(2023)
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arxiv(2022)
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user-5dd52aee530c701191bf1b99(2022)
Stat. Comput.no. 1 (2022)
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