On the Forward Filtering Backward Smoothing particle approximations of the smoothing distribution in general state spaces models
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.
- Publication:
-
arXiv e-prints
- Pub Date:
- April 2009
- DOI:
- 10.48550/arXiv.0904.0316
- arXiv:
- arXiv:0904.0316
- Bibcode:
- 2009arXiv0904.0316D
- Keywords:
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- Mathematics - Statistics;
- 60G10;
- 60K35;
- 60G18