Iterative ensemble smoothers in the annealed importance sampling framework

- 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.

Iterative ensemble techniques for solving inverse problems has recently gained a lot of interest in many geophysical communities. This popularity is attributed to the simplicity of implementation, general reliability and the ability to deal with the forward model as a black box without requiring the implementation of analytical gradients. Although several variants exist, we focus on the ensemble smoother with multiple data assimilation. This study highlights the similarity between the ensemble smoother and other existing techniques such as particle flow and annealed importance sampling. It is shown how a sequential Monte Carlo sampler can be used in combination with an annealing process to weight-correct the sampling procedure used in the ensemble smoother. Two different approximations in high dimensions, where the curse of dimensionality is unavoidable, are also presented. The methods proposed are compared with an MCMC run on a synthetic reservoir model.