Sequential ensemble transform for Bayesian inverse problems

We present the Sequential Ensemble Transform (SET) method, an approach for generating approximate samples from a Bayesian posterior distribution. The method explores distribution by solving sequence of discrete optimal transport problems to produce series plans which map prior samples. prove that Dirac mixture distributions produced SET converges weakly true as sample size approaches infinity. Furthermore, our numerical results indicate that, when compared standard Monte Carlo (SMC) methods, is more robust choice Markov mutation kernels and requires less computational efforts reach similar accuracy used explore complex distributions. Finally, we describe adaptive schemes allow completely automate use method.