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Rao-Blackwellisation of particle Markov chain Monte Carlo methods using forward filtering backward sampling

Olsson, Jimmy LU and Rydén, Tobias LU (2011) In IEEE Transactions on Signal Processing 59(10). p.4606-4619
Abstract (Swedish)
Abstract in Undetermined

Smoothing in state-space models amounts to computing the conditional distribution of the latent state trajectory, given observations, or expectations of functionals of the state trajectory with respect to this distribution. In recent years there has been an increased interest in Monte Carlo-based methods, often involving particle filters, for approximate smoothing in nonlinear and/or non-Gaussian state-space models. One such method is to approximate filter distributions using a particle filter and then to simulate, using backward kernels, a state trajectory backwards on the set of particles. We show that by simulating multiple realizations of the particle filter and adding a Metropolis-Hastings... (More)
Abstract in Undetermined

Smoothing in state-space models amounts to computing the conditional distribution of the latent state trajectory, given observations, or expectations of functionals of the state trajectory with respect to this distribution. In recent years there has been an increased interest in Monte Carlo-based methods, often involving particle filters, for approximate smoothing in nonlinear and/or non-Gaussian state-space models. One such method is to approximate filter distributions using a particle filter and then to simulate, using backward kernels, a state trajectory backwards on the set of particles. We show that by simulating multiple realizations of the particle filter and adding a Metropolis-Hastings step, one obtains a Markov chain Monte Carlo scheme whose stationary distribution is the exact smoothing distribution. This procedure expands upon a similar one recently proposed by Andrieu, Doucet, Holenstein, and Whiteley. We also show that simulating multiple trajectories from each realization of the particle filter can be beneficial from a perspective of variance versus computation time, and illustrate this idea using two examples. (Less)
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author
organization
publishing date
type
Contribution to journal
publication status
published
subject
keywords
Hidden Markov models, Trajectory, Smoothing methods, Signal processing algorithms, Markov processes, Kernel, Joints
in
IEEE Transactions on Signal Processing
volume
59
issue
10
pages
4606 - 4619
publisher
IEEE--Institute of Electrical and Electronics Engineers Inc.
external identifiers
  • wos:000297111500009
  • scopus:80052890727
ISSN
1053-587X
DOI
10.1109/TSP.2011.2161296
language
English
LU publication?
yes
id
f2bba21a-64b6-476b-ad55-a1fc139ef777 (old id 2224264)
date added to LUP
2012-01-19 12:12:42
date last changed
2017-05-07 03:12:20
@article{f2bba21a-64b6-476b-ad55-a1fc139ef777,
  abstract     = {<b>Abstract in Undetermined</b><br/><br>
Smoothing in state-space models amounts to computing the conditional distribution of the latent state trajectory, given observations, or expectations of functionals of the state trajectory with respect to this distribution. In recent years there has been an increased interest in Monte Carlo-based methods, often involving particle filters, for approximate smoothing in nonlinear and/or non-Gaussian state-space models. One such method is to approximate filter distributions using a particle filter and then to simulate, using backward kernels, a state trajectory backwards on the set of particles. We show that by simulating multiple realizations of the particle filter and adding a Metropolis-Hastings step, one obtains a Markov chain Monte Carlo scheme whose stationary distribution is the exact smoothing distribution. This procedure expands upon a similar one recently proposed by Andrieu, Doucet, Holenstein, and Whiteley. We also show that simulating multiple trajectories from each realization of the particle filter can be beneficial from a perspective of variance versus computation time, and illustrate this idea using two examples.},
  author       = {Olsson, Jimmy and Rydén, Tobias},
  issn         = {1053-587X},
  keyword      = {Hidden Markov models,Trajectory,Smoothing methods,Signal processing algorithms,Markov processes,Kernel,Joints},
  language     = {eng},
  number       = {10},
  pages        = {4606--4619},
  publisher    = {IEEE--Institute of Electrical and Electronics Engineers Inc.},
  series       = {IEEE Transactions on Signal Processing},
  title        = {Rao-Blackwellisation of particle Markov chain Monte Carlo methods using forward filtering backward sampling},
  url          = {http://dx.doi.org/10.1109/TSP.2011.2161296},
  volume       = {59},
  year         = {2011},
}