Sensitivity analysis for finite Markov chains in discrete time
Gert de Cooman, Filip Hermans, Erik Quaeghebeur
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 socalled 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 socalled lower and upper expectations. We also study how the inferred credal set about the state at time n evolves as n>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 nontrivial generalisation of the classical PerronFrobenius Theorem to imprecise Markov chains.
Keywords: null
Pages: 129136
PS Link:
PDF Link: /papers/08/p129de_cooman.pdf
BibTex:
@INPROCEEDINGS{de Cooman08,
AUTHOR = "Gert de Cooman
and Filip Hermans and Erik Quaeghebeur",
TITLE = "Sensitivity analysis for finite Markov chains in discrete time",
BOOKTITLE = "Proceedings of the TwentyFourth Conference Annual Conference on Uncertainty in Artificial Intelligence (UAI08)",
PUBLISHER = "AUAI Press",
ADDRESS = "Corvallis, Oregon",
YEAR = "2008",
PAGES = "129136"
}

