Abstract
If the state space of a homogeneous continuous-time Markov chain is too large, making inferences—here limited to determining marginal or limit expectations—becomes computationally infeasible. Fortunately, the state space of such a chain is usually too detailed for the inferences we are interested in, in the sense that a less detailed—smaller—state space suffices to unambiguously formalise the inference. However, in general this so-called lumped state space inhibits computing exact inferences because the corresponding dynamics are unknown and/or intractable to obtain. We address this issue by considering an imprecise continuous-time Markov chain. In this way, we are able to provide guaranteed lower and upper bounds for the inferences of interest, without suffering from the curse of dimensionality.
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Notes
- 1.
We use
and 
to denote the set of non-negative real numbers and positive real numbers, respectively. Furthermore, we use 
to denote the natural numbers and write 
when including zero.
and 
to denote the set of non-negative real numbers and positive real numbers, respectively. Furthermore, we use 
to denote the natural numbers and write 
when including zero.References
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Acknowledgements
Jasper De Bock’s research was partially funded by H2020-MSCA-ITN-2016 UTOPIAE, grant agreement 722734. Furthermore, the authors are grateful to the reviewers for their constructive feedback and useful suggestions.
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Erreygers, A., De Bock, J. (2019). Computing Inferences for Large-Scale Continuous-Time Markov Chains by Combining Lumping with Imprecision. In: Destercke, S., Denoeux, T., Gil, M., Grzegorzewski, P., Hryniewicz, O. (eds) Uncertainty Modelling in Data Science. SMPS 2018. Advances in Intelligent Systems and Computing, vol 832. Springer, Cham. https://doi.org/10.1007/978-3-319-97547-4_11
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