Bayesian smoothing algorithms in partially observed Markov Chains

Boujemaa Ait El Fquih*, François Desbouvries

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


Let x = xnn∈N be a hidden process, y = y nn∈N an observed process and r = rn n∈N some auxiliary process. We assume that t = t nn∈N 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, these smoothers reduce to a set of algorithms which include, among other solutions, extensions to TMC of classical Kalman-like smoothing algorithms (originally designed for HMC) such as the RTS algorithms, the Two-Filter algorithms or the Bryson and Frazier algorithm.

Original languageEnglish (US)
Pages (from-to)339-346
Number of pages8
JournalAIP Conference Proceedings
StatePublished - Dec 27 2006


  • Bayesian restoration
  • Gauss-Markov chains
  • Hidden Markov models

ASJC Scopus subject areas

  • Ecology, Evolution, Behavior and Systematics
  • Ecology
  • Plant Science
  • Physics and Astronomy(all)
  • Nature and Landscape Conservation


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