### Abstract

A practical approach to statistical inference for hidden Markov models (HMMs) requires expressions for the mean and variance of the log-probability of an observed T-long sequence given the model parameters. From the viewpoint of Shannon theory, in the limit of large T, the expected value of the per step log-probability is minus one times the mean entropy rate at the output of a noisy channel driven by the Markov source. A novel procedure for finding the entropy rate is presented. The rate distortion function of the Markov source, subject to the requirement of instantaneous coding, is a by-product of the derivation.

Original language | English |
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Title of host publication | Proceedings - 1998 IEEE International Symposium on Information Theory, ISIT 1998 |

Number of pages | 1 |

DOIs | |

Publication status | Published - 1998 |

Event | 1998 IEEE International Symposium on Information Theory, ISIT 1998 - Cambridge, MA, United States Duration: 1998 Aug 16 → 1998 Aug 21 |

### Publication series

Name | IEEE International Symposium on Information Theory - Proceedings |
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ISSN (Print) | 2157-8095 |

### Other

Other | 1998 IEEE International Symposium on Information Theory, ISIT 1998 |
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Country | United States |

City | Cambridge, MA |

Period | 98/8/16 → 98/8/21 |

### ASJC Scopus subject areas

- Theoretical Computer Science
- Information Systems
- Modelling and Simulation
- Applied Mathematics

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## Cite this

Ko, H., & Baran, R. H. (1998). Entropy and information rates for hidden Markov models. In

*Proceedings - 1998 IEEE International Symposium on Information Theory, ISIT 1998*[708979] (IEEE International Symposium on Information Theory - Proceedings). https://doi.org/10.1109/ISIT.1998.708979