Ensemble transport smoothing. Part I: Unified framework

Understand

Smoothers are algorithms for Bayesian time series re-analysis.

• Most operational smoothers rely either on affine Kalman-type transformations or on sequential importance sampling.
• These strategies occupy opposite ends of a spectrum that trades computational efficiency and scalability for statistical generality and consistency: non-Gaussianity renders affine Kalman updates inconsistent with the true Bayesian solution, while the ensemble size required for successful importance sampling can be prohibitive.
• This paper revisits the smoothing problem from the perspective of measure transport, which offers the prospect of consistent prior-to-posterior transformations for Bayesian inference.