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Sensitivity analysis for finite Markov chains in discrete time

Gert De Cooman (UGent) , Filip Hermans (UGent) and Erik Quaeghebeur (UGent)
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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 Perron–Frobenius Theorem to imprecise Markov chains.

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Chicago
De Cooman, Gert, Filip Hermans, and Erik Quaeghebeur. 2008. “Sensitivity Analysis for Finite Markov Chains in Discrete Time.” In Uncertainty in Artificial Intelligence: Proceedings of the Twenty-Fourth Conference, ed. D McAllester and P Myllymäki, 129–136.
APA
De Cooman, Gert, Hermans, F., & Quaeghebeur, E. (2008). Sensitivity analysis for finite Markov chains in discrete time. In D. McAllester & P. Myllymäki (Eds.), Uncertainty in Artificial Intelligence: Proceedings of the Twenty-Fourth Conference (pp. 129–136). Presented at the UAI 2008: Twenty-Fourth Conference of Uncertainty in Artificial Intelligence.
Vancouver
1.
De Cooman G, Hermans F, Quaeghebeur E. Sensitivity analysis for finite Markov chains in discrete time. In: McAllester D, Myllymäki P, editors. Uncertainty in Artificial Intelligence: Proceedings of the Twenty-Fourth Conference. 2008. p. 129–36.
MLA
De Cooman, Gert, Filip Hermans, and Erik Quaeghebeur. “Sensitivity Analysis for Finite Markov Chains in Discrete Time.” Uncertainty in Artificial Intelligence: Proceedings of the Twenty-Fourth Conference. Ed. D McAllester & P Myllymäki. 2008. 129–136. Print.
@inproceedings{427340,
  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 Perron--Frobenius Theorem to imprecise Markov chains.},
  author       = {De Cooman, Gert and Hermans, Filip and Quaeghebeur, Erik},
  booktitle    = {Uncertainty in Artificial Intelligence: Proceedings of the Twenty-Fourth Conference},
  editor       = {McAllester, D and Myllym{\"a}ki, P},
  isbn         = {0-9749039-4-9},
  language     = {eng},
  location     = {Helsinki, Fnland},
  pages        = {129--136},
  title        = {Sensitivity analysis for finite Markov chains in discrete time},
  url          = {http://dx.doi.org/1854/11638},
  year         = {2008},
}

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