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Sequential Monte Carlo smoothing for general state space hidden Markov models

Douc, Randal; Garivier, Aurelien; Moulines, Eric and Olsson, Jimmy LU (2011) In Annals of Applied Probability 21(6). p.2109-2145
Abstract
Computing smoothing distributions, the distributions of one or more states conditional on past, present, and future observations is a recurring problem when operating on general hidden Markov models. The aim of this paper is to provide a foundation of particle-based approximation of such distributions and to analyze, in a common unifying framework, different schemes producing such approximations. In this setting, general convergence results, including exponential deviation inequalities and central limit theorems, are established. In particular, time uniform bounds on the marginal smoothing error are obtained under appropriate mixing conditions on the transition kernel of the latent chain. In addition, we propose an algorithm approximating... (More)
Computing smoothing distributions, the distributions of one or more states conditional on past, present, and future observations is a recurring problem when operating on general hidden Markov models. The aim of this paper is to provide a foundation of particle-based approximation of such distributions and to analyze, in a common unifying framework, different schemes producing such approximations. In this setting, general convergence results, including exponential deviation inequalities and central limit theorems, are established. In particular, time uniform bounds on the marginal smoothing error are obtained under appropriate mixing conditions on the transition kernel of the latent chain. In addition, we propose an algorithm approximating the joint smoothing distribution at a cost that grows only linearly with the number of particles. (Less)
Please use this url to cite or link to this publication:
author
organization
publishing date
type
Contribution to journal
publication status
published
subject
keywords
Sequential Monte Carlo methods, particle filter, smoothing, hidden, Markov models
in
Annals of Applied Probability
volume
21
issue
6
pages
2109 - 2145
publisher
Institute of Mathematical Statistics
external identifiers
  • wos:000298249900003
  • scopus:82655181336
ISSN
1050-5164
DOI
10.1214/10-AAP735
language
English
LU publication?
yes
id
1a390e18-b4ac-4979-a391-e58dd6912215 (old id 2333239)
date added to LUP
2012-02-06 13:54:11
date last changed
2017-10-22 04:18:45
@article{1a390e18-b4ac-4979-a391-e58dd6912215,
  abstract     = {Computing smoothing distributions, the distributions of one or more states conditional on past, present, and future observations is a recurring problem when operating on general hidden Markov models. The aim of this paper is to provide a foundation of particle-based approximation of such distributions and to analyze, in a common unifying framework, different schemes producing such approximations. In this setting, general convergence results, including exponential deviation inequalities and central limit theorems, are established. In particular, time uniform bounds on the marginal smoothing error are obtained under appropriate mixing conditions on the transition kernel of the latent chain. In addition, we propose an algorithm approximating the joint smoothing distribution at a cost that grows only linearly with the number of particles.},
  author       = {Douc, Randal and Garivier, Aurelien and Moulines, Eric and Olsson, Jimmy},
  issn         = {1050-5164},
  keyword      = {Sequential Monte Carlo methods,particle filter,smoothing,hidden,Markov models},
  language     = {eng},
  number       = {6},
  pages        = {2109--2145},
  publisher    = {Institute of Mathematical Statistics},
  series       = {Annals of Applied Probability},
  title        = {Sequential Monte Carlo smoothing for general state space hidden Markov models},
  url          = {http://dx.doi.org/10.1214/10-AAP735},
  volume       = {21},
  year         = {2011},
}