Fokker-Planck particle systems for Bayesian inference: computational approaches
- Bayesian inference can be embedded into an appropriately defined dynamics in the space of probability measures. In this paper, we take Brownian motion and its associated Fokker-Planck equation as a starting point for such embeddings and explore several interacting particle approximations. More specifically, we consider both deterministic and stochastic interacting particle systems and combine them with the idea of preconditioning by the empirical covariance matrix. In addition to leading to affine invariant formulations which asymptotically speed up convergence, preconditioning allows for gradient-free implementations in the spirit of the ensemble Kalman filter. While such gradient-free implementations have been demonstrated to work well for posterior measures that are nearly Gaussian, we extend their scope of applicability to multimodal measures by introducing localized gradient-free approximations. Numerical results demonstrate the effectiveness of the considered methodologies.
Author details: | Sebastian ReichORCiDGND, Simon WeissmannORCiD |
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DOI: | https://doi.org/10.1137/19M1303162 |
ISSN: | 2166-2525 |
Title of parent work (English): | SIAM ASA journal on uncertainty quantification |
Publisher: | Society for Industrial and Applied Mathematics |
Place of publishing: | Philadelphia |
Publication type: | Article |
Language: | English |
Date of first publication: | 2021/01/01 |
Publication year: | 2021 |
Release date: | 2023/11/30 |
Tag: | Bayesian inverse problems; Fokker-Planck equation; affine; gradient flow; gradient-free sampling methods; invariance; localization |
Volume: | 9 |
Issue: | 2 |
Number of pages: | 37 |
First page: | 446 |
Last Page: | 482 |
Funding institution: | Deutsche Forschungsgemeinschaft (DFG, German Science Foundation) German Research Foundation (DFG) [SFB 1294/1-318763901]; DFGGerman Research Foundation (DFG)European Commission [RTG1953]; state of Baden-Wurttemberg through bwHPC |
Organizational units: | Mathematisch-Naturwissenschaftliche Fakultät / Institut für Mathematik |
DDC classification: | 5 Naturwissenschaften und Mathematik / 51 Mathematik / 510 Mathematik |
Peer review: | Referiert |