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Bounding inferences for large-scale continuous-time Markov chains: A new approach based on lumping and imprecise Markov chains

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 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.
Keywords
lumping, imprecise Markov chain, state space explosion

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Citation

Please use this url to cite or link to this publication:

MLA
Erreygers, Alexander, and Jasper De Bock. “Bounding Inferences for Large-scale Continuous-time Markov Chains: A New Approach Based on Lumping and Imprecise Markov Chains.” International Journal of Approximate Reasoning 115 (2019): 96–133. Print.
APA
Erreygers, A., & De Bock, J. (2019). Bounding inferences for large-scale continuous-time Markov chains: A new approach based on lumping and imprecise Markov chains. International Journal of Approximate Reasoning, 115, 96–133.
Chicago author-date
Erreygers, Alexander, and Jasper De Bock. 2019. “Bounding Inferences for Large-scale Continuous-time Markov Chains: A New Approach Based on Lumping and Imprecise Markov Chains.” International Journal of Approximate Reasoning 115: 96–133.
Chicago author-date (all authors)
Erreygers, Alexander, and Jasper De Bock. 2019. “Bounding Inferences for Large-scale Continuous-time Markov Chains: A New Approach Based on Lumping and Imprecise Markov Chains.” International Journal of Approximate Reasoning 115: 96–133.
Vancouver
1.
Erreygers A, De Bock J. Bounding inferences for large-scale continuous-time Markov chains: A new approach based on lumping and imprecise Markov chains. International Journal of Approximate Reasoning. Elsevier; 2019;115:96–133.
IEEE
[1]
A. Erreygers and J. De Bock, “Bounding inferences for large-scale continuous-time Markov chains: A new approach based on lumping and imprecise Markov chains,” International Journal of Approximate Reasoning, vol. 115, pp. 96–133, 2019.
@article{8629728,
  abstract     = {If the state space of a homogeneous continuous-time Markov chain is too large, making inferences 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},
  issn         = {0888-613X},
  journal      = {International Journal of Approximate Reasoning},
  keywords     = {lumping,imprecise Markov chain,state space explosion},
  language     = {eng},
  pages        = {96--133},
  publisher    = {Elsevier},
  title        = {Bounding inferences for large-scale continuous-time Markov chains: A new approach based on lumping and imprecise Markov chains},
  url          = {http://dx.doi.org/10.1016/j.ijar.2019.09.003},
  volume       = {115},
  year         = {2019},
}

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