The seventy-seventh UQSay seminar on UQ, DACE and related topics will take place online on Thursday afternoon, October 31, 2024.
2–3 PM — Nadège Polette (Mines Paris PSL - CEA DAM DIF) — [slides]
Mitigating Overconfidence in Bayesian Field Inversion thanks to Hyperparameters Sampling
The objective of Bayesian field inversion is to approximate the posterior distribution of a field thanks to indirect observations. Such problems have to face two issues, the infinite dimensionality of the field and the high number of forward model evaluations required to achieve MCMC convergence. In this study, the field to infer is assumed to be a particular realization of a random field and is modeled by its truncated Karhunen-Loève (KL) decomposition leading to a finite dimensional parametrization. The KL representation relies on an autocovariance function that depends on poorly known hyperparameters. The added value of our work is to introduce a new method, called change of measure, designed to deal with uncertain hyperparameters instead of deterministic ones. In practice, the hyperparameters are jointly sampled with the KL coordinates and the posterior distribution has a hierarchical Bayesian structure. In addition, to reduce the computational cost of the MCMC procedure, the likelihood is estimated with polynomial chaos surrogates of the forward model outputs. Applications on transient diffusion and seismic traveltime tomography problems highlight the interest of not fixing the hyperparameters to deterministic values. Exploring the hyperparameters space is highly valuable because it provides a better estimation of the field uncertainties.
References:
Joint work with O. Le Maître (CNRS, CMAP) & P. Sochala (CEA DAM DIF) & A. Gesret (Mines Paris PSL).
Organizing committee: Pierre Barbillon (MIA-Paris), Julien Bect (L2S), Nicolas Bousquet (EDF R&D), Vincent Chabridon (EDF R&D), Amélie Fau (LMPS), Filippo Gatti (LMPS), Clément Gauchy (CEA), Bertrand Iooss (EDF R&D), Alexandre Janon (LMO), Sidonie Lefebvre (ONERA), Didier Lucor (LISN), Sébastien Petit (LNE), Emmanuel Vazquez (L2S), Xujia Zhu (L2S).
Coordinators: Sidonie Lefebvre (ONERA) & Xujia Zhu (L2S)
Practical details: the seminar will be held online using Microsoft Teams.
If you want to attend this seminar (or any of the forthcoming online UQSay seminars), and if you do not already have access to the UQSay group on Teams, simply send an email and you will be invited. Please specify which email address the invitation must be sent to (this has to be the address associated with your Teams account).
You will find the link to the seminar on the "General" UQSay channel on Teams, approximately 15 minutes before the beginning.
The technical side of things: you can use Teams either directly from your web browser or using the "fat client", which is available for most platforms (Windows, Linux, Mac, Android & iOS). We strongly recommend the latter option whenever possible. Please give it a try before the seminar to anticipate potential problems.
