Exact and approximate Bayesian smoothing algorithms in partially observed Markov Chains

Boujemaa Ait-el-Fquih; François Desbouvries

doi:10.1109/NSSPW.2006.4378841

Exact and approximate Bayesian smoothing algorithms in partially observed Markov Chains

Boujemaa Ait-el-Fquih^*, François Desbouvries

^*Corresponding author for this work

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

3 Scopus citations

Abstract

Let x = {x_n}_n∈IN be a hidden process, y = {y_n}_n∈IN an observed process and r = {r _n}_n∈IN some auxiliary process. We assume that t = {t_n}_n∈IN with t_n = (x_n, r _n, y_n-1) is a (Triplet) Markov Chain (TMC). TMC are more general than Hidden Markov Chains (HMC) and yet enable the development of efficient restoration and parameter estimation algorithms. This paper is devoted to Bayesian smoothing algorithms for TMC. We first propose twelve algorithms for general TMC. In the Gaussian case, they reduce to a set of algorithms which includes, among other solutions, extensions to TMC of classical Kalman-like smoothing algorithms such as the RTS algorithms, the Two-Filter algorithm or the Bryson and Frazier algorithm. We finally propose particle filtering (PF) approximations for the general case.

Original language	English (US)
Title of host publication	NSSPW - Nonlinear Statistical Signal Processing Workshop 2006
Publisher	IEEE Computer Society
Pages	148-151
Number of pages	4
ISBN (Print)	1424405815, 9781424405817
DOIs	https://doi.org/10.1109/NSSPW.2006.4378841
State	Published - 2006
Externally published	Yes
Event	NSSPW - Nonlinear Statistical Signal Processing Workshop 2006 - Cambridge, United Kingdom Duration: Sep 13 2006 → Sep 15 2006

Publication series

Name	NSSPW - Nonlinear Statistical Signal Processing Workshop 2006

Other

Other	NSSPW - Nonlinear Statistical Signal Processing Workshop 2006
Country/Territory	United Kingdom
City	Cambridge
Period	09/13/06 → 09/15/06

ASJC Scopus subject areas

Signal Processing
Statistics, Probability and Uncertainty
Electrical and Electronic Engineering
Statistics and Probability

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10.1109/NSSPW.2006.4378841

Cite this

@inproceedings{4f73a22fc8024d30a866b36d9b3f52ee,

title = "Exact and approximate Bayesian smoothing algorithms in partially observed Markov Chains",

abstract = "Let x = {xn}n∈IN be a hidden process, y = {yn}n∈IN an observed process and r = {r n}n∈IN some auxiliary process. We assume that t = {tn}n∈IN with tn = (xn, r n, yn-1) is a (Triplet) Markov Chain (TMC). TMC are more general than Hidden Markov Chains (HMC) and yet enable the development of efficient restoration and parameter estimation algorithms. This paper is devoted to Bayesian smoothing algorithms for TMC. We first propose twelve algorithms for general TMC. In the Gaussian case, they reduce to a set of algorithms which includes, among other solutions, extensions to TMC of classical Kalman-like smoothing algorithms such as the RTS algorithms, the Two-Filter algorithm or the Bryson and Frazier algorithm. We finally propose particle filtering (PF) approximations for the general case.",

author = "Boujemaa Ait-el-Fquih and Fran{\c c}ois Desbouvries",

year = "2006",

doi = "10.1109/NSSPW.2006.4378841",

language = "English (US)",

isbn = "1424405815",

series = "NSSPW - Nonlinear Statistical Signal Processing Workshop 2006",

publisher = "IEEE Computer Society",

pages = "148--151",

booktitle = "NSSPW - Nonlinear Statistical Signal Processing Workshop 2006",

address = "United States",

note = "NSSPW - Nonlinear Statistical Signal Processing Workshop 2006 ; Conference date: 13-09-2006 Through 15-09-2006",

}

Ait-el-Fquih, B & Desbouvries, F 2006, Exact and approximate Bayesian smoothing algorithms in partially observed Markov Chains. in NSSPW - Nonlinear Statistical Signal Processing Workshop 2006., 4378841, NSSPW - Nonlinear Statistical Signal Processing Workshop 2006, IEEE Computer Society, pp. 148-151, NSSPW - Nonlinear Statistical Signal Processing Workshop 2006, Cambridge, United Kingdom, 09/13/06. https://doi.org/10.1109/NSSPW.2006.4378841

Exact and approximate Bayesian smoothing algorithms in partially observed Markov Chains. / Ait-el-Fquih, Boujemaa; Desbouvries, François.
NSSPW - Nonlinear Statistical Signal Processing Workshop 2006. IEEE Computer Society, 2006. p. 148-151 4378841 (NSSPW - Nonlinear Statistical Signal Processing Workshop 2006).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

TY - GEN

T1 - Exact and approximate Bayesian smoothing algorithms in partially observed Markov Chains

AU - Ait-el-Fquih, Boujemaa

AU - Desbouvries, François

PY - 2006

Y1 - 2006

N2 - Let x = {xn}n∈IN be a hidden process, y = {yn}n∈IN an observed process and r = {r n}n∈IN some auxiliary process. We assume that t = {tn}n∈IN with tn = (xn, r n, yn-1) is a (Triplet) Markov Chain (TMC). TMC are more general than Hidden Markov Chains (HMC) and yet enable the development of efficient restoration and parameter estimation algorithms. This paper is devoted to Bayesian smoothing algorithms for TMC. We first propose twelve algorithms for general TMC. In the Gaussian case, they reduce to a set of algorithms which includes, among other solutions, extensions to TMC of classical Kalman-like smoothing algorithms such as the RTS algorithms, the Two-Filter algorithm or the Bryson and Frazier algorithm. We finally propose particle filtering (PF) approximations for the general case.

AB - Let x = {xn}n∈IN be a hidden process, y = {yn}n∈IN an observed process and r = {r n}n∈IN some auxiliary process. We assume that t = {tn}n∈IN with tn = (xn, r n, yn-1) is a (Triplet) Markov Chain (TMC). TMC are more general than Hidden Markov Chains (HMC) and yet enable the development of efficient restoration and parameter estimation algorithms. This paper is devoted to Bayesian smoothing algorithms for TMC. We first propose twelve algorithms for general TMC. In the Gaussian case, they reduce to a set of algorithms which includes, among other solutions, extensions to TMC of classical Kalman-like smoothing algorithms such as the RTS algorithms, the Two-Filter algorithm or the Bryson and Frazier algorithm. We finally propose particle filtering (PF) approximations for the general case.

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DO - 10.1109/NSSPW.2006.4378841

M3 - Conference contribution

AN - SCOPUS:48049103010

SN - 1424405815

SN - 9781424405817

T3 - NSSPW - Nonlinear Statistical Signal Processing Workshop 2006

SP - 148

EP - 151

BT - NSSPW - Nonlinear Statistical Signal Processing Workshop 2006

PB - IEEE Computer Society

T2 - NSSPW - Nonlinear Statistical Signal Processing Workshop 2006

Y2 - 13 September 2006 through 15 September 2006

ER -

Exact and approximate Bayesian smoothing algorithms in partially observed Markov Chains

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