Sensitivity analysis for finite Markov chains in discrete time

Gert De Cooman, Filip Hermans, Erik Quaeghebeur

Research output: Chapter in Book/Report/Conference proceedingConference contributionAcademicpeer-review

6 Citations (Scopus)

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 languageEnglish
Title of host publicationProceedings of the 24th Conference on Uncertainty in Artificial Intelligence, UAI 2008
EditorsDavid A. McAllester, Petri Myllymäki
Pages129-136
Number of pages8
DOIs
Publication statusPublished - 2008
Externally publishedYes
Event24th Conference on Uncertainty in Artificial Intelligence, UAI 2008 - Helsinki, Finland
Duration: 9 Jul 200812 Jul 2008

Conference

Conference24th Conference on Uncertainty in Artificial Intelligence, UAI 2008
Country/TerritoryFinland
CityHelsinki
Period9/07/0812/07/08

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