SBIA '02 Proceedings of the 16th Brazilian Symposium on Artificial Intelligence: Advances in Artificial Intelligence
Robust Control of Markov Decision Processes with Uncertain Transition Matrices
Operations Research
Partially observable Markov decision processes with imprecise parameters
Artificial Intelligence
Imprecise probability trees: Bridging two theories of imprecise probability
Artificial Intelligence
Imprecise markov chains and their limit behavior
Probability in the Engineering and Informational Sciences
Imprecise Markov chains with absorption
International Journal of Approximate Reasoning
International Journal of Approximate Reasoning
The use of Markov operators to constructing generalised probabilities
International Journal of Approximate Reasoning
Probabilistic model checking of biological systems with uncertain kinetic rates
Theoretical Computer Science
Information Sciences: an International Journal
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The parameters of Markov chain models are often not known precisely. Instead of ignoring this problem, a better way to cope with it is to incorporate the imprecision into the models. This has become possible with the development of models of imprecise probabilities, such as the interval probability model. In this paper we discuss some modelling approaches which range from simple probability intervals to the general interval probability models and further to the models allowing completely general convex sets of probabilities. The basic idea is that precisely known initial distributions and transition matrices are replaced by imprecise ones, which effectively means that sets of possible candidates are considered. Consequently, sets of possible results are obtained and represented using similar imprecise probability models. We first set up the model and then show how to perform calculations of the distributions corresponding to the consecutive steps of a Markov chain. We present several approaches to such calculations and compare them with respect to the accuracy of the results. Next we consider a generalisation of the concept of regularity and study the convergence of regular imprecise Markov chains. We also give some numerical examples to compare different approaches to calculations of the sets of probabilities.