| Description |
This seminar provides an overview of uncertainty quantification methods, bridging the gap between theory and application. Participants will consolidate their knowledge of mathematical/statistical underlying principles while reading and presenting selected book chapters and methodological articles, leading to discussions that effectively link theory and practice. To further strengthen the bridging focus, the seminar aims to involve participants (and invited experts) from both statistics and applied fields, such as geosciences and epidemiology.
The following topics are on the agenda:
I) Inverse problems
- Introduction to inverse problems, deterministic versus Bayesian inversion
- Gaussian approximation and variational inference
- Monte Carlo and importance sampling, Markov chain Monte Carlo methods
II) Data assimilation
- Introduction to filtering and smoothing problems
- (Extended) Kalman filter and ensemble Kalman filter
Theoretical backbone
Sanz-Alonso, D., Stuart, A., & Taeb, A. (2023). Inverse Problems and Data Assimilation. Cambridge: Cambridge University Press.
Some example methodological and application papers (to be discussed at semester start)
Bui-Thanh, T., Ghattas, O., Martin, J., & Stadler, G. (2013). A computational framework for infinite-dimensional Bayesian inverse problems Part I: The linearized case, with application to global seismic inversion. SIAM Journal on Scientific Computing, 35(6), A2494-A2523
Course, K., Nair, P.B. (2023) State estimation of a physical system with unknown governing equations. Nature 622, 261–267
Dumont Le Brazidec J., Bocquet M., Saunier O., Roustan Y. (2021). Quantification of the modelling uncertainties in atmospheric release source assessment and application to the reconstruction of the autumn 2017 Ruthenium 106 source. Atmos. Chem. Phys., pp. 1-28
Huang, D.Z.; Schneider, T.; Stuart, A. M. (2022). Iterated Kalman methodology for inverse problems. Journal of Computational Physics. Volume 463, 15 August 2022, 111262
Piazzola, C., Tamellini, L., Tempone, R. (2020). A note on tools for prediction under uncertainty and identifiability of SIR-like dynamical systems for epidemiology. Mathematical Biosciences 332, 108514
Sung, C.L. (2022). Estimating functional parameters for understanding the impact of weather and government interventions on COVID-19 outbreak. Ann. Appl. Stat. 16(4): 2505-2522 |
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