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Abstract
We present an algorithm that can efficiently compute a broad class of inferences for discrete-time imprecise Markov chains, a generalised type of Markov chains that allows one to take into account partially specified probabilities and other types of model uncertainty. The class of inferences that we consider contains, as special cases, tight lower and upper bounds on expected hitting times, on hitting probabilities and on expectations of functions that are a sum or product of simpler ones. Our algorithm exploits the specific structure that is inherent in all these inferences: they admit a general recursive decomposition. This allows us to achieve a computational complexity that scales linearly in the number of time points on which the inference depends, instead of the exponential scaling that is typical for a naive approach.
Keywords
Imprecise Markov chains, Upper and lower expectations, Recursively decomposable inferences

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MLA
T’Joens, Natan, et al. “A Recursive Algorithm for Computing Inferences in Imprecise Markov Chains.” Symbolic and Quantitative Approaches to Reasoning with Uncertainty, 15th European Conference, ECSQARU 2019, Belgrade, Serbia, September 18-20, 2019, Proceedings, edited by Gabriele Kern-Isberner and Zoran Ognjanović, vol. 11726, Springer, 2019, pp. 455–65.
APA
T’Joens, N., Krak, T., De Bock, J., & De Cooman, G. (2019). A recursive algorithm for computing inferences in imprecise Markov chains. In G. Kern-Isberner & Z. Ognjanović (Eds.), Symbolic and quantitative approaches to reasoning with uncertainty, 15th European Conference, ECSQARU 2019, Belgrade, Serbia, September 18-20, 2019, Proceedings (Vol. 11726, pp. 455–465). Belgrade, Serbia: Springer.
Chicago author-date
T’Joens, Natan, Thomas Krak, Jasper De Bock, and Gert De Cooman. 2019. “A Recursive Algorithm for Computing Inferences in Imprecise Markov Chains.” In Symbolic and Quantitative Approaches to Reasoning with Uncertainty, 15th European Conference, ECSQARU 2019, Belgrade, Serbia, September 18-20, 2019, Proceedings, edited by Gabriele Kern-Isberner and Zoran Ognjanović, 11726:455–65. Springer.
Chicago author-date (all authors)
T’Joens, Natan, Thomas Krak, Jasper De Bock, and Gert De Cooman. 2019. “A Recursive Algorithm for Computing Inferences in Imprecise Markov Chains.” In Symbolic and Quantitative Approaches to Reasoning with Uncertainty, 15th European Conference, ECSQARU 2019, Belgrade, Serbia, September 18-20, 2019, Proceedings, ed by. Gabriele Kern-Isberner and Zoran Ognjanović, 11726:455–465. Springer.
Vancouver
1.
T’Joens N, Krak T, De Bock J, De Cooman G. A recursive algorithm for computing inferences in imprecise Markov chains. In: Kern-Isberner G, Ognjanović Z, editors. Symbolic and quantitative approaches to reasoning with uncertainty, 15th European Conference, ECSQARU 2019, Belgrade, Serbia, September 18-20, 2019, Proceedings. Springer; 2019. p. 455–65.
IEEE
[1]
N. T’Joens, T. Krak, J. De Bock, and G. De Cooman, “A recursive algorithm for computing inferences in imprecise Markov chains,” in Symbolic and quantitative approaches to reasoning with uncertainty, 15th European Conference, ECSQARU 2019, Belgrade, Serbia, September 18-20, 2019, Proceedings, Belgrade, Serbia, 2019, vol. 11726, pp. 455–465.
@inproceedings{8629186,
  abstract     = {We present an algorithm that can efficiently compute a broad class of inferences for discrete-time imprecise Markov chains, a generalised type of Markov chains that allows one to take into account partially specified probabilities and other types of model uncertainty. The class of inferences that we consider contains, as special cases, tight lower and upper bounds on expected hitting times, on hitting probabilities and on expectations of functions that are a sum or product of simpler ones. Our algorithm exploits the specific structure that is inherent in all these inferences: they admit a general recursive decomposition. This allows us to achieve a computational complexity that scales linearly in the number of time points on which the inference depends, instead of the exponential scaling that is typical for a naive approach.},
  author       = {T'Joens, Natan and Krak, Thomas and De Bock, Jasper and De Cooman, Gert},
  booktitle    = {Symbolic and quantitative approaches to reasoning with uncertainty, 15th European Conference, ECSQARU 2019, Belgrade, Serbia, September 18-20, 2019, Proceedings},
  editor       = {Kern-Isberner, Gabriele and Ognjanović, Zoran},
  isbn         = {9783030297640},
  issn         = {0302-9743},
  keywords     = {Imprecise Markov chains,Upper and lower expectations,Recursively decomposable inferences},
  language     = {eng},
  location     = {Belgrade, Serbia},
  pages        = {455--465},
  publisher    = {Springer},
  title        = {A recursive algorithm for computing inferences in imprecise Markov chains},
  url          = {http://dx.doi.org/10.1007/978-3-030-29765-7_38},
  volume       = {11726},
  year         = {2019},
}

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