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

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

2009-04-02

arxiv.org/abs/0904.0316v1

Mathematics

Statistics Theory

Scientific paper

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.

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