@inproceedings{GdC-2008-UAI,
author = {De Cooman, Gert and Hermans, Filip and Quaeghebeur, Erik},
editor = {McAllester, D. and MyllymĂ¤ki, P.},
title = {Sensitivity analysis for finite Markov chains in discrete time},
booktitle = {Uncertainty in Artificial Intelligence: Proceedings of the Twenty-Fourth Conference},
year = {2008},
venue = {Helsinki, Fnland},
eventdate = {2008-07-09/2008-07-12},
eventtitle = {UAI 2008: Twenty-Fourth Conference of Uncertainty in Artificial Intelligence},
organization = {AUAI},
pages = {129--136},
url = {http://hdl.handle.net/1854/11638},
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 goes to infinity: 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 Perronâ€“Frobenius Theorem to imprecise Markov chains.
},
isbn = {0-9749039-4-9},
}