Measures of uncertainty in expert systems
Artificial Intelligence
How good are convex hull algorithms?
Computational Geometry: Theory and Applications
Artificial Intelligence
The Art of Causal Conjecture
Epistemic irrelevance on sets of desirable gambles
Annals of Mathematics and Artificial Intelligence
Robust Control of Markov Decision Processes with Uncertain Transition Matrices
Operations Research
Partially observable Markov decision processes with imprecise parameters
Artificial Intelligence
Marginal extension in the theory of coherent lower previsions
International Journal of Approximate Reasoning
Imprecise probability trees: Bridging two theories of imprecise probability
Artificial Intelligence
Graphical models for imprecise probabilities
International Journal of Approximate Reasoning
Discrete time Markov chains with interval probabilities
International Journal of Approximate Reasoning
Epistemic irrelevance in credal nets: The case of imprecise Markov trees
International Journal of Approximate Reasoning
Imprecise Markov chains with absorption
International Journal of Approximate Reasoning
Characterisation of ergodic upper transition operators
International Journal of Approximate Reasoning
Information Sciences: an International Journal
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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 can be 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, which are equivalent mathematical representations of credal sets. 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 generalization of the classical Perron–Frobenius theorem to imprecise Markov chains.