Particle approximation improvement of the joint smoothing distribution with on-the-fly variance estimation

2011/07/27 by Cyrille Dubarry, Randal Douc, Dubarry, Cyrille +1 · 1 citation
Computer Science · Mathematics · #Bayesian Methods and Mixture Models #FOS: Computer and information sciences #Methodology (stat.ME) #Statistical Methods and Bayesian Inference #Target Tracking and Data Fusion in Sensor Networks #stat.ME

paper · pdf · doi:10.48550/arxiv.1107.5524

arxiv created 2011/07/27 · openalex publication_date 2011/07/27 · arxiv updated 2011/07/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Particle smoothers are widely used algorithms allowing to approximate the smoothing distribution in hidden Markov models. Existing algorithms often suffer from slow computational time or degeneracy. We propose in this paper a way to improve any of them with a linear complexity in the number of particles. When iteratively applied to the degenerated Filter-Smoother, this method leads to an algorithm which turns out to outperform existing linear particle smoothers for a fixed computational time. Moreover, the associated approximation satisfies a central limit theorem with a close-to-optimal asymptotic variance, which be easily estimated by only one run of the algorithm.

Citations

• Metropolising forward particle filtering backward sampling and Rao-Blackwellisation of Metropolised particle smoothers
• SMC²: an efficient algorithm for sequential analysis of state-space models
• Central limit theorem for sequential Monte Carlo methods and its application to Bayesian inference

Cited by

• An extended space approach for particle Markov chain Monte Carlo methods

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