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Uncertainty Quantification and Modern Statistical Inference

Periodic Reporting for period 3 - UQMSI (Uncertainty Quantification and Modern Statistical Inference)

Reporting period: 2018-09-01 to 2020-02-29

The objectives are the understanding the mathematical underpinnings of modern statistical inference techniques and uncertainty quantification procedures. As such methodology is widely used in sciences/medicine etc it has great long term impact on society. Research on the topics suggested in the grant proposal, and dissemination of research results at conferences.

Several research papers have been written and submitted by summer 2018, some already published (see the publications page for details). The main focus has been on obtaining rigorous mathematical results that justify the use of Bayesian statistical methodology for inference with complex and high-dimensional data generating processes, such as nonlinear inverse problems arising with PDEs or jump processes. Further work in this direction is on the way. We also obtained some results about high-dimensional statistics (for matrix completion, principal component analysis) of a non-Bayesian nature.
Research on the topics suggested in the grant proposal, and dissemination of research results at conferences.
Substantially new results on the understanding of matrix completion procedures, and of Bayesian inference methods for diffusion models, were obtained. Other related projects are currently ongoing.