We show how the Ensemble Smoother with multiple data assimilation can be formulated in an importance sampling framework.

The algorithm can be formulated as an iterative Monte Carlo method using ideas from annealed importance sampling and sequential Monte Carlo samplers.

A hybrid version of the algorithm is proposed using Gaussian mixtures to alleviate some of the bias of the original algorithm.

The proposed algorithms are tested on a subsurface inverse problem which indicates that the Gaussian mixture approach can improve upon the existing algorithm.