Ensemble transport smoothing. Part I: Unified framework

Maximilian Ramgraber, Ricardo Baptista, Dennis McLaughlin, Youssef Marzouk

Research output: Contribution to journalArticleScientificpeer-review

1 Citation (Scopus)


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. We leverage this capacity by proposing a general ensemble framework for transport-based smoothing. Within this framework, we derive a comprehensive set of smoothing recursions based on nonlinear transport maps and detail how they exploit the structure of state-space models in fully non-Gaussian settings. We also describe how many standard Kalman-type smoothing algorithms emerge as special cases of our framework. A companion paper [35] explores the implementation of nonlinear ensemble transport smoothers in greater depth.

Original languageEnglish
Article number100134
JournalJournal of Computational Physics: X
Publication statusPublished - Nov 2023
Externally publishedYes


Dive into the research topics of 'Ensemble transport smoothing. Part I: Unified framework'. Together they form a unique fingerprint.

Cite this