Iterative Bayesian inversion with Gaussian mixtures: finite sample implementation and large sample asymptotics

摘要

Approximate solutions for Bayesian estimation in large scale models is a topic under investigation in many scientific communities. We define an iterative method based on the adaptive Gaussian mixture filter with batch updates as a robust alternative to adaptive importance sampling. We prove asymptotic optimality under certain conditions, contrary to other methods discussed where the sample distribution depends on the nonlinearity and scaling of the model. The finite sample implementation of the method is compared to an ensemble smoother with multiple data assimilation and an ensemble-based randomized maximum likelihood approach on a synthetic 1D reservoir model.