Fokker-Planck particle systems for Bayesian inference: Computational approaches

Understand

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.