Open Access
August 2017 Efficient particle-based online smoothing in general hidden Markov models: The PaRIS algorithm
Jimmy Olsson, Johan Westerborn
Bernoulli 23(3): 1951-1996 (August 2017). DOI: 10.3150/16-BEJ801


This paper presents a novel algorithm, the particle-based, rapid incremental smoother (PaRIS), for efficient online approximation of smoothed expectations of additive state functionals in general hidden Markov models. The algorithm, which has a linear computational complexity under weak assumptions and very limited memory requirements, is furnished with a number of convergence results, including a central limit theorem. An interesting feature of PaRIS, which samples on-the-fly from the retrospective dynamics induced by the particle filter, is that it requires two or more backward draws per particle in order to cope with degeneracy of the sampled trajectories and to stay numerically stable in the long run with an asymptotic variance that grows only linearly with time.


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Jimmy Olsson. Johan Westerborn. "Efficient particle-based online smoothing in general hidden Markov models: The PaRIS algorithm." Bernoulli 23 (3) 1951 - 1996, August 2017.


Received: 1 December 2014; Revised: 1 September 2015; Published: August 2017
First available in Project Euclid: 17 March 2017

zbMATH: 06714324
MathSciNet: MR3624883
Digital Object Identifier: 10.3150/16-BEJ801

Keywords: central limit theorem , general hidden Markov models , Hoeffding-type inequality , online estimation , particle filter , particle path degeneracy , sequential Monte Carlo , smoothing

Rights: Copyright © 2017 Bernoulli Society for Mathematical Statistics and Probability

Vol.23 • No. 3 • August 2017
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