Hidden semi-Markov model

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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 Leonard E. Baum and Ted 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.


  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, doi:10.1239/jap/1085496598 .
  3. ^ Barbu, V.; Limnios, N. (2008). "Hidden Semi-Markov Model and Estimation". Semi-Markov Chains and Hidden Semi-Markov Models toward Applications. Lecture Notes in Statistics 191. p. 1. doi:10.1007/978-0-387-73173-5_6. ISBN 978-0-387-73171-1.  edit
  4. ^ Baum, L. E.; Petrie, T. (1966). "Statistical Inference for Probabilistic Functions of Finite State Markov Chains". The Annals of Mathematical Statistics 37 (6): 1554. doi:10.1214/aoms/1177699147.  edit

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