Ensemble transport smoothing. Part I: Unified framework

• URL: http://arxiv.org/abs/2210.17000v2
• Date: Wed, 22 Nov 2023 15:17:40 GMT
• Title: Ensemble transport smoothing. Part I: Unified framework
• Authors: Maximilian Ramgraber, Ricardo Baptista, Dennis McLaughlin, Youssef Marzouk
• Abstract summary: We propose a general ensemble framework for transport-based smoothing. We detail how they exploit the structure of state-space models in fully non-Gaussian settings. A companion paper explores the implementation of nonlinear ensemble transport smoothers in greater depth.
• Score: 0.40964539027092906
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: 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 (Ramgraber et al., 2023) explores the implementation of nonlinear ensemble transport smoothers in greater depth.

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