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Research Area A

Research Area A focuses on the theoretical and algorithmic foundation of data assimilation. In case of a data-rich situation (e.g.~fully observed processes) and finite-dimensional estimation problems, there is a well-developed theory available. The situation changes fundamentally when one moves from such well-posed to ill-posed statistical inverse problems, i.e., towards partially observed processes and/or infinite-dimensional estimation problems (non-parametric statistics), where there are many open mathematical problems and algorithmic challenges.

A01 - Statistics for stochastic partial differential equations

The project will contribute to the emerging field of statistics of SPDEs by both looking at general principles of statistical inference for SPDEs.

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A02 - Long-time stability and accuracy of ensemble transform filter algorithms

The project will investigate the long time stability and accuracy of sequential probabilistic filtering algorithms for state estimation.

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A03 - Sequential and adaptive learning under dependence and non-standard objective functions

We aim to design strategies to collect (or to sample) sequentially and adaptively the data so that it can be assimilated by models.

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A04 - Nonlinear statistical inverse problems with random observations

The project is concerned with the non-parametric estimation of covariate effects on time-dependent processes.

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A05 - Combining non parametric statistical and probabilistic approaches for inference on ...

The main research goal of this project is to explore certain classes of point processes such as Gibbsian processes for modelling

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A06 - Approximative Bayesian inference and model selection for stochastic differential equations.

This project is concerned with semi-parametric and fully nonparametric approaches for estimating drift functions in systems of stochastic DE.

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