Sequential Ensemble Transform for Bayesian Inverse Problems
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We present the Sequential Ensemble Transform (SET) method, a new approach for generating approximate samples from a Bayesian posterior distribution. The method explores the posterior by solving a sequence of discrete linear optimal transport problems to produce a series of transport plans which map prior samples to posterior samples. We show that the sequence of Dirac mixture distributions produced by the SET method converges weakly to the true posterior as the sample size approaches infinity. Our numerical results indicate that, as opposed to more standard Sequential Monte Carlo (SMC) methods used for inference in Bayesian inverse problems, the SET approach is more robust to the choice of Markov mutation kernel steps.
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