Imprecise Continuous-Time Markov Chains: Efficient Computational Methods with Guaranteed Error Bounds

Alexander Erreygers, Jasper De Bock
; Proceedings of the Tenth International Symposium on Imprecise Probability: Theories and Applications, PMLR 62:145-156, 2017.

Abstract

Imprecise continuous-time Markov chains are a robust type of continuous-time Markov chains that allow for partially specified time-dependent parameters. Computing inferences for them requires the solution of a non-linear differential equation. As there is no general analytical expression for this solution, efficient numerical approximation methods are essential to the applicability of this model. We here improve the uniform approximation method of Krak et al. (2016) in two ways and propose a novel and more efficient adaptive approximation method. For ergodic chains, we also provide a method that allows us to approximate stationary distributions up to any desired maximal error.

Cite this Paper


BibTeX
@InProceedings{pmlr-v62-erreygers17a, title = {Imprecise Continuous-Time {M}arkov Chains: Efficient Computational Methods with Guaranteed Error Bounds}, author = {Alexander Erreygers and Jasper De Bock}, booktitle = {Proceedings of the Tenth International Symposium on Imprecise Probability: Theories and Applications}, pages = {145--156}, year = {2017}, editor = {Alessandro Antonucci and Giorgio Corani and Inés Couso and Sébastien Destercke}, volume = {62}, series = {Proceedings of Machine Learning Research}, month = {10--14 Jul}, publisher = {PMLR}, pdf = {http://proceedings.mlr.press/v62/erreygers17a/erreygers17a.pdf}, url = {http://proceedings.mlr.press/v62/erreygers17a.html}, abstract = {Imprecise continuous-time Markov chains are a robust type of continuous-time Markov chains that allow for partially specified time-dependent parameters. Computing inferences for them requires the solution of a non-linear differential equation. As there is no general analytical expression for this solution, efficient numerical approximation methods are essential to the applicability of this model. We here improve the uniform approximation method of Krak et al. (2016) in two ways and propose a novel and more efficient adaptive approximation method. For ergodic chains, we also provide a method that allows us to approximate stationary distributions up to any desired maximal error.} }
Endnote
%0 Conference Paper %T Imprecise Continuous-Time Markov Chains: Efficient Computational Methods with Guaranteed Error Bounds %A Alexander Erreygers %A Jasper De Bock %B Proceedings of the Tenth International Symposium on Imprecise Probability: Theories and Applications %C Proceedings of Machine Learning Research %D 2017 %E Alessandro Antonucci %E Giorgio Corani %E Inés Couso %E Sébastien Destercke %F pmlr-v62-erreygers17a %I PMLR %J Proceedings of Machine Learning Research %P 145--156 %U http://proceedings.mlr.press %V 62 %W PMLR %X Imprecise continuous-time Markov chains are a robust type of continuous-time Markov chains that allow for partially specified time-dependent parameters. Computing inferences for them requires the solution of a non-linear differential equation. As there is no general analytical expression for this solution, efficient numerical approximation methods are essential to the applicability of this model. We here improve the uniform approximation method of Krak et al. (2016) in two ways and propose a novel and more efficient adaptive approximation method. For ergodic chains, we also provide a method that allows us to approximate stationary distributions up to any desired maximal error.
APA
Erreygers, A. & De Bock, J.. (2017). Imprecise Continuous-Time Markov Chains: Efficient Computational Methods with Guaranteed Error Bounds. Proceedings of the Tenth International Symposium on Imprecise Probability: Theories and Applications, in PMLR 62:145-156

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