## Abstract

When the initial and transition probabilities of a finite Markov chain in discrete time are not well known, we should perform a sensitivity analysis. This is done by considering as basic uncertainty models the so-called credal sets that these probabilities are known or believed to belong to, and by allowing the probabilities to vary over such sets. This leads to the definition of an imprecise Markov chain. We show that the time evolution of such a system can be studied very efficiently using so-called lower and upper expectations. We also study how the inferred credal set about the state at time n evolves as n → ∞: under quite unrestrictive conditions, it converges to a uniquely invariant credal set, regardless of the credal set given for the initial state. This leads to a non-trivial generalisation of the classical Perron-Frobenius Theorem to imprecise Markov chains.

Original language | English |
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Title of host publication | Proceedings of the 24th Conference on Uncertainty in Artificial Intelligence, UAI 2008 |

Editors | David A. McAllester, Petri Myllymäki |

Pages | 129-136 |

Number of pages | 8 |

DOIs | |

Publication status | Published - 2008 |

Externally published | Yes |

Event | 24th Conference on Uncertainty in Artificial Intelligence, UAI 2008 - Helsinki, Finland Duration: 9 Jul 2008 → 12 Jul 2008 |

### Conference

Conference | 24th Conference on Uncertainty in Artificial Intelligence, UAI 2008 |
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Country/Territory | Finland |

City | Helsinki |

Period | 9/07/08 → 12/07/08 |