Fast and Numerically Stable Particle-Based Online Additive Smoothing: The AdaSmooth Algorithm

Alessandro Mastrototaro, Jimmy Olsson and Johan Alenlöv

Journal of the American Statistical Association, 2024, vol. 119, issue 545, 356-367

Abstract: We present a novel sequential Monte Carlo approach to online smoothing of additive functionals in a very general class of path-space models. Hitherto, the solutions proposed in the literature suffer from either long-term numerical instability due to particle-path degeneracy or, in the case that degeneracy is remedied by particle approximation of the so-called backward kernel, high computational demands. In order to balance optimally computational speed against numerical stability, we propose to furnish a (fast) naive particle smoother, propagating recursively a sample of particles and associated smoothing statistics, with an adaptive backward-sampling-based updating rule which allows the number of (costly) backward samples to be kept at a minimum. This yields a new, function-specific additive smoothing algorithm, AdaSmooth, which is computationally fast, numerically stable and easy to implement. The algorithm is provided with rigorous theoretical results guaranteeing its consistency, asymptotic normality and long-term stability as well as numerical results demonstrating empirically the clear superiority of AdaSmooth to existing algorithms. Supplementary materials for this article are available online.

Date: 2024
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DOI: 10.1080/01621459.2022.2118602

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