Past Event: CSEM Student Forum

An Efficient Sequential Optimal Transport method for Bayesian inverse problems

Aaron Myers, CSEM, ICES, UT Austin

Abstract

We present the Sequential Ensemble Transform (SET) method for generating approximate samples from a posterior distribution as a solution to Bayesian inverse problems. The method explores the posterior by solving a sequence of discrete, linear optimal transport problems, resulting in a series of transport maps which map prior samples to posterior samples. This allows us to efficiently characterize statistical properties of quantities of interest, quantify uncertainty, and compute moments. We present theory proving that the sequence of Dirac mixture distributions generated by the SET method converges to the true posterior. Numerically, we show this method can offer superior computational efficiency when compared to resampling-based Sequential Monte Carlo (SMC) methods in the regime of low mutation steps and small ensemble size; the regime where particle degeneracy is likely to occur.