TY - JOUR
T1 - Ensemble transport smoothing. Part I: Unified framework
AU - Ramgraber, Maximilian
AU - Baptista, Ricardo
AU - McLaughlin, Dennis
AU - Marzouk, Youssef
PY - 2023/11
Y1 - 2023/11
N2 - 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.
AB - 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.
UR - http://www.scopus.com/inward/record.url?scp=85176922888&partnerID=8YFLogxK
U2 - 10.1016/j.jcpx.2023.100134
DO - 10.1016/j.jcpx.2023.100134
M3 - Article
SN - 2590-0552
VL - 17
JO - Journal of Computational Physics: X
JF - Journal of Computational Physics: X
M1 - 100134
ER -