On the Forward Filtering Backward Smoothing particle approximations of the smoothing distribution in general state spaces models

2009/04/02 by Randal Douc, Aurélien Garivier, Douc, Randal +5 · 1 citation
Computer Science · #60G10 #60G18 #60K35 #Bayesian Methods and Mixture Models #Distributed Sensor Networks and Detection Algorithms #FOS: Mathematics #Statistics Theory (math.ST) #Target Tracking and Data Fusion in Sensor Networks

paper · pdf · doi:10.48550/arxiv.0904.0316

openalex publication_date 2009/04/02 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

A prevalent problem in general state-space models is the approximation of the smoothing distribution of a state, or a sequence of states, conditional on the observations from the past, the present, and the future. The aim of this paper is to provide a rigorous foundation for the calculation, or approximation, of such smoothed distributions, and to analyse in a common unifying framework different schemes to reach this goal. Through a cohesive and generic exposition of the scientific literature we offer several novel extensions allowing to approximate joint smoothing distribution in the most general case with a cost growing linearly with the number of particles.

Citations

• Central limit theorem for sequential Monte Carlo methods and its application to Bayesian inference

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• Compositional meta-learning through probabilistic task inference

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