Sequential Monte Carlo smoothing for general state space hidden Markov models
(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:
https://lup.lub.lu.se/record/2333239
- author
- Douc, Randal ; Garivier, Aurelien ; Moulines, Eric and Olsson, Jimmy LU
- organization
- publishing date
- 2011
- 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
- 2016-04-01 14:21:02
- date last changed
- 2022-03-29 20:24:08
@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}},
keywords = {{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}},
doi = {{10.1214/10-AAP735}},
volume = {{21}},
year = {{2011}},
}