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 spec...
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| Main Authors: | , |
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| Format: | Article (Journal) |
| Language: | English |
| Published: |
April 26, 2021
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| In: |
SIAM ASA journal on uncertainty quantification
Year: 2021, Volume: 9, Issue: 2, Pages: 446-482 |
| ISSN: | 2166-2525 |
| DOI: | 10.1137/19M1303162 |
| Online Access: | Verlag, lizenzpflichtig, Volltext: https://doi.org/10.1137/19M1303162 Verlag, lizenzpflichtig, Volltext: https://epubs.siam.org/doi/10.1137/19M1303162 
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| Author Notes: | Sebastian Reich and Simon Weissmann |
| Summary: | 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. |
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| Item Description: | Gesehen am 04.09.2021 |
| Physical Description: | Online Resource |
| ISSN: | 2166-2525 |
| DOI: | 10.1137/19M1303162 |