CMX Lunch Seminar

Bayesian Inversion consists of deriving the posterior distribution of unknown parameters or functions from partial and indirect observations of a system. When the dimension of the search space is high or infinite, methods leveraging local information, such as derivatives of different orders, of the target probability measure have the advantages to converge faster than Monte-Carlo sampling techniques. Nevertheless, many applications are characterized by posterior distributions with low regularity or gradients that are intractable to compute. An interesting research direction consists in using interacting particle systems to explore the potential landscape, and Ensemble Kalman Sampler (EKS) is one of those. In this talk, we consider a simplified EKS dynamics, where the gradient of the potential is approximated by finite differences using independent Ornstein-Uhlenbeck processes that explore the neighborhood of the candidate parameter. We will characterize the invariant distribution of this system and compare its dynamics to the overdamped Langevin process.