Hidden semi-Markov model: Difference between revisions

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A hidden semi-Markov model (HSMM) is a statistical model with the same structure as a hidden Markov model except that the unobservable process is semi-Markov rather than Markov. This means that the probability of there being a change in the hidden state depends on the amount of time that has elapsed since entry into the current state. This is in contrast to hidden Markov models where there is a constant probability of changing state given survival in the state up to that time.^[1]

For instance Sanson & Thomson (2001) modelled daily rainfall using a hidden semi-Markov model.^[2] If the underlying process (e.g. weather system) does not have a geometrically distributed duration, an HSMM may be more appropriate.

The model was first published by Baum and Petrie in 1966.^[3]^[4]

Statistical inference for hidden semi-Markov models is more difficult than in hidden Markov models, since algorithms like the Baum-Welch algorithm are not directly applicable, and must be adapted requiring more resources.

References

^ Yu, Shun-Zheng, "Hidden Semi-Markov Models", Artificial Intelligence, 174 (2): 215–243, doi:10.1016/j.artint.2009.11.011.
^ Sansom, J.; Thomson, P. J. (2001), "Fitting hidden semi-Markov models to breakpoint rainfall data", J. Appl. Probab., 38A: 142–157.
^ Attention: This template ({{cite doi}}) is deprecated. To cite the publication identified by doi:10.1007/978-0-387-73173-5_6, please use {{cite journal}} (if it was published in a bona fide academic journal, otherwise {{cite report}} with |doi=10.1007/978-0-387-73173-5_6 instead.
^ Attention: This template ({{cite doi}}) is deprecated. To cite the publication identified by doi:10.1214/aoms/1177699147, please use {{cite journal}} (if it was published in a bona fide academic journal, otherwise {{cite report}} with |doi=10.1214/aoms/1177699147 instead.

Additional reading

Guédon, Y. (2003), "Estimating hidden semi-Markov chains from discrete sequences", Journal of Computational and Graphical Statistics, 12 (3): 604–639.
Murphy, Kevin P. (2002), Hidden semi-Markov Models (HSMMs) (PDF)
Liu, X. L.; Liang, Y.; Lou, Y. H.; Li, H.; Shan, B. S. (2010), "Noise-Robust Voice Activity Detector Based on Hidden Semi-Markov Models", Proc. ICPR'10 (PDF), pp. 81–84.
Bulla, J.; Bulla, I.; Nenadiç, O. (2010), "hsmm – an R Package for Analyzing Hidden Semi-Markov Models", Computational Statistics & Data Analysis, 54 (3): 611–619.

External links

Shun-Zheng Yu, HSMM – Online bibliography and Matlab source code

This statistics-related article is a stub. You can help Wikipedia by expanding it.

[1] Yu, Shun-Zheng, "Hidden Semi-Markov Models", Artificial Intelligence, 174 (2): 215–243, doi:10.1016/j.artint.2009.11.011.

[2] Sansom, J.; Thomson, P. J. (2001), "Fitting hidden semi-Markov models to breakpoint rainfall data", J. Appl. Probab., 38A: 142–157.

[3] Attention: This template ({{cite doi}}) is deprecated. To cite the publication identified by doi:10.1007/978-0-387-73173-5_6, please use {{cite journal}} (if it was published in a bona fide academic journal, otherwise {{cite report}} with |doi=10.1007/978-0-387-73173-5_6 instead.

[4] Attention: This template ({{cite doi}}) is deprecated. To cite the publication identified by doi:10.1214/aoms/1177699147, please use {{cite journal}} (if it was published in a bona fide academic journal, otherwise {{cite report}} with |doi=10.1214/aoms/1177699147 instead.

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 For instance {{harvtxt|Sanson|Thomson|2001}} modelled daily rainfall using a hidden semi-Markov model.<ref>{{citation|first1=J.|last1=Sansom|first2=P. J.|last2=Thomson|title=Fitting hidden semi-Markov models to breakpoint rainfall data|journal=J. Appl. Probab.|volume=38A|year=2001|pages=142–157}}.</ref> If the underlying process (e.g. weather system) does not have a [[geometric distribution|geometrically distributed]] duration, an HSMM may be more appropriate.
+The model was first published by Baum and Petrie in 1966.<ref>{{cite doi|10.1007/978-0-387-73173-5_6}}</ref><ref>{{cite doi|10.1214/aoms/1177699147}}</ref>
 Statistical inference for hidden semi-Markov models is more difficult than in hidden Markov models, since algorithms like the [[Baum-Welch algorithm]] are not directly applicable, and must be adapted requiring more resources.