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Ensemble Kalman Inversion (EnKI) and Ensemble Square Root Filter (EnSRF) are popular sampling methods for obtaining a target posterior distribution. They can be seem as one step (the analysis step) in the data assimilation method Ensemble Kalman Filter. Despite their popularity, they are, however, not unbiased when the forward map is nonlinear. Important Sampling (IS), on the other hand, obtains the unbiased sampling at the expense of large variance of weights, leading to slow convergence of high moments. We propose WEnKI and WEnSRF, the weight
We present a novel algorithm based on the ensemble Kalman filter to solve inverse problems involving multiscale elliptic partial differential equations. Our method is based on numerical homogenization and finite element discretization and allows to r
Several numerical tools designed to overcome the challenges of smoothing in a nonlinear and non-Gaussian setting are investigated for a class of particle smoothers. The considered family of smoothers is induced by the class of linear ensemble transfo
A useful approach to solve inverse problems is to pair the parameter-to-data map with a stochastic dynamical system for the parameter, and then employ techniques from filtering to estimate the parameter given the data. Three classical approaches to f
In this work we marry multi-index Monte Carlo with ensemble Kalman filtering (EnKF) to produce the multi-index EnKF method (MIEnKF). The MIEnKF method is based on independent samples of four-coupled EnKF estimators on a multi-index hierarchy of resol
Ensemble Kalman Sampler (EKS) is a method to find approximately $i.i.d.$ samples from a target distribution. As of today, why the algorithm works and how it converges is mostly unknown. The continuous version of the algorithm is a set of coupled stoc