TY  - JOUR
A1  - Reich, Sebastian
A1  - Weissmann, Simon
T1  - Fokker-Planck particle systems for Bayesian inference: computational approaches
JF  - SIAM ASA journal on uncertainty quantification
N2  - 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.
KW  - Bayesian inverse problems
KW  - Fokker-Planck equation
KW  - gradient flow
KW  - affine
KW  - invariance
KW  - gradient-free sampling methods
KW  - localization
Y1  - 2021
U6  - https://doi.org/10.1137/19M1303162
SN  - 2166-2525
VL  - 9
IS  - 2
SP  - 446
EP  - 482
PB  - Society for Industrial and Applied Mathematics
CY  - Philadelphia
ER  -