Duration: 2017 - 2021
Funded by: HORIZON 2020
About: UTOPIAE is a training and research network funded by the European Commission hrough the H2020 funding scheme. The main objectives of this network are to train, by research and by example, 15 Early Stage Researchers (ESRs) in the field of Uncertainty Quantification (UQ) and Optimization and to impart them the skills to become leading independent researchers and entrepreneurs that will increase the EU innovation capacity. These skills will enable the ESRs to pursue careers in academia and industry. Through individual research projects, each ESR will investigate different facets of UQ and Optimization Under Uncertainty and develop cutting-edge methods and algorithms with particular focus on aerospace applications.
This project (ESR9) is running at the Durham University Partner Site under the umbrella of the UTOPIAE network.
Supervisors: Dr Jochen Einbeck and Dr Matthias Troffaes.
This project is concerned with statistical inference for highly dimensional data with limited structural knowledge. The specific character of such situations would be (i) the data structure is too complex to describe the data through parametric models (ii) the dimension is too high too describe the data through nonparametric or sufficiently flexible semiparametric models (iii) even if either (i) or (ii) was feasible, there is considerable uncertainty on the type of structure and interaction which the data to be modelled exhibit; partly due to overwhelming complexity or lack of data.
This project will take a unified Bayesian-frequentist viewpoint, employing adequate regularization techniques which aim at sparse model representations through appropriate priors or penalties, respectively. To quantify the uncertainty of the resulting estimates, methods from imprecise probability will be investigated, which can be considered as the natural cutpoint between the Bayesian and the frequentist paradigm. In this context, we will investigate how standard statistical simulation approaches, such as for instance Markov chain Monte Carlo, can be extended to do inference from highly dimensional data, in a way that leads to computationally efficient yet still reliable inference about the actual risks in the system; to derive theoretical results from small scale tests; to upscale the dimensionality of the application, depending on the results of the small scale tests.
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This project has received funding from the biggest European Union Research and Innovation Programme Horizon 2020 HORIZON 2020 Website