Ensemble Kalman Sampler

Abstract

Many modern inverse problems are based upon a very complex forward model that is computationally expensive. In such a setting, numerical estimation of a gradient can be instable or infeasible and derivative-free solution methods are preferred. This thesis studies the Ensemble Kalman Sampler (EKS), a novel algorithm that samples from the posterior of a Bayesian inverse problem using no information of the gradient. EKS is based upon Langevin dynamics and is a noisy variation of Ensemble Kalman Inversion (EKI). The new noise structure causes EKS to effectively sample from the posterior, instead of collapsing to a single optimal point like EKI. Two numerical results are presented to demonstrate the algorithm’s effectiveness.