| 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. |
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