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Computing inferences for large-scale continuous-time Markov chains by combining lumping with imprecision

Alexander Erreygers (UGent) and Jasper De Bock (UGent)
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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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Chicago
Erreygers, Alexander, and Jasper De Bock. 2018. “Computing Inferences for Large-scale Continuous-time Markov Chains by Combining Lumping with Imprecision.” In Uncertainty Modelling in Data Science, ed. Sébastien Destercke, Thierry Denoeux, María Ángeles Gil, Przemyslaw Gregorzewski, and Olgierd Hryniewicz, 832:78–86. Cham, Switzerland: Springer International Publishing.
APA
Erreygers, Alexander, & De Bock, J. (2018). Computing inferences for large-scale continuous-time Markov chains by combining lumping with imprecision. In S. Destercke, T. Denoeux, M. Á. Gil, P. Gregorzewski, & O. Hryniewicz (Eds.), Uncertainty Modelling in Data Science (Vol. 832, pp. 78–86). Presented at the 9th International Conference on Soft Methods in Probability and Statistics, Cham, Switzerland: Springer International Publishing.
Vancouver
1.
Erreygers A, De Bock J. Computing inferences for large-scale continuous-time Markov chains by combining lumping with imprecision. In: Destercke S, Denoeux T, Gil MÁ, Gregorzewski P, Hryniewicz O, editors. Uncertainty Modelling in Data Science. Cham, Switzerland: Springer International Publishing; 2018. p. 78–86.
MLA
Erreygers, Alexander, and Jasper De Bock. “Computing Inferences for Large-scale Continuous-time Markov Chains by Combining Lumping with Imprecision.” Uncertainty Modelling in Data Science. Ed. Sébastien Destercke et al. Vol. 832. Cham, Switzerland: Springer International Publishing, 2018. 78–86. Print.
@inproceedings{8575677,
  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.},
  author       = {Erreygers, Alexander and De Bock, Jasper},
  booktitle    = {Uncertainty Modelling in Data Science},
  editor       = {Destercke, Sébastien and Denoeux, Thierry and Gil, María Ángeles and Gregorzewski, Przemyslaw and Hryniewicz, Olgierd},
  isbn         = {9783319975467},
  issn         = {2194-5357},
  language     = {eng},
  location     = {Compiègne, France},
  pages        = {78--86},
  publisher    = {Springer International Publishing},
  title        = {Computing inferences for large-scale continuous-time Markov chains by combining lumping with imprecision},
  url          = {http://dx.doi.org/10.1007/978-3-319-97547-4_11},
  volume       = {832},
  year         = {2018},
}

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