The Ensemble Kalman Filter for Rare Event Estimation

We present a novel sampling-based method for estimating probabilities of rare or failure events. Our approach is founded on the ensemble Kalman filter (EnKF) inverse problems. Therefore, we reformulate event problem as an and apply EnKF to generate samples. To estimate probability failure, use final samples fit distribution model importance sampling with respect fitted distribution. This leads unbiased estimator if density admits positive values within whole domain. handle multimodal domains, localize covariance matrices in update step around each particle mixture step. For affine linear limit-state functions, investigate continuous time limit large properties update. prove that mean particles converges convex combination most likely point optimal applied without noise. provide numerical experiments compare performance sequential sampling.