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.
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References
De Bock, J.: Credal networks under epistemic irrelevance. Int. J. Approximate Reasoning 85, 107–138 (2017)
De Bock, J.: Credal networks under epistemic irrelevance: theory and algorithms. Ph.D. thesis, Ghent University (2015)
de Cooman, G., Hermans, F.: Imprecise probability trees: bridging two theories of imprecise probability. Artif. Intell. 172(11), 1400–1427 (2008)
de Cooman, G., Hermans, F., Antonucci, A., Zaffalon, M.: Epistemic irrelevance in credal nets: the case of imprecise Markov trees. Int. J. Approximate Reasoning 51(9), 1029–1052 (2010)
de Cooman, G., Hermans, F., Quaeghebeur, E.: Imprecise Markov chains and their limit behaviour. Probab. Eng. Inf. Sci. 23(4), 597–635 (2009)
Hermans, F., Škulj, D.: Stochastic processes. In: Augustin, T., Coolen, F.P.A., De Cooman, G., Troffaes, M.C.M. (eds.) Introduction to Imprecise Probabilities. Wiley (2014). Chapter 11
Kallenberg, O.: Foundations of Modern Probability. Springer Science & Business Media, New York (2006)
Krak, T’Joens, N., De Bock, J.: Hitting times and probabilities for imprecise Markov chains (2019). Accepted for publication in the conference proceedings of ISIPTA 2019. A preprint can be found at arXiv:1905.08781
Lopatatzidis, S.: Robust Modelling and Optimisation in Stochastic Processes using Imprecise Probabilities, with an Application to Queueing Theory. Ph.D. thesis, Ghent University (2017)
Shafer, G., Vovk, V.: Probability and Finance: It’s Only a Game!. Wiley, New York (2001)
T’Joens, N., De Bock, J., de Cooman, G.: In search of a global belief model for discrete-time uncertain processes (2019). Accepted for publication in the conference proceedings of ISIPTA 2019
T’Joens, N., De Bock, J., de Cooman, G.: Continuity properties of game-theoretic upper expectations. arXiv:1902.09406 (2019)
T’Joens, N., Krak, T., De Bock, J., de Cooman, G.: A Recursive Algorithm for Computing Inferences in Imprecise Markov Chains. arXiv:1905.12968 (2019)
Acknowledgments
The work in this paper was partially supported by H2020-MSCA-ITN-2016 UTOPIAE, grant agreement 722734.
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T’Joens, N., Krak, T., Bock, J.D., Cooman, G.d. (2019). A Recursive Algorithm for Computing Inferences in Imprecise Markov Chains. In: Kern-Isberner, G., Ognjanović, Z. (eds) Symbolic and Quantitative Approaches to Reasoning with Uncertainty. ECSQARU 2019. Lecture Notes in Computer Science(), vol 11726. Springer, Cham. https://doi.org/10.1007/978-3-030-29765-7_38
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DOI: https://doi.org/10.1007/978-3-030-29765-7_38
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