Robust Model Checking with Imprecise Markov Reward Models

Alberto Termine, Alessandro Antonucci, Alessandro Facchini, Giuseppe Primiero
Proceedings of the Twelveth International Symposium on Imprecise Probability: Theories and Applications, PMLR 147:299-309, 2021.

Abstract

In recent years probabilistic model checking has become an important area of research because of the diffusion of computational systems of stochastic nature. Despite its great success, standard probabilistic model checking suffers the limitation of requiring a sharp specification of the probabilities governing the model behaviour. The theory of imprecise probabilities offers a natural approach to overcome such limitation by a sensitivity analysis with respect to the values of these parameters. However, only extensions based on discrete-time imprecise Markov chains have been considered so far for such a robust approach to model checking. We present a further extension based on imprecise Markov reward models. In particular, we derive efficient algorithms to compute lower and upper bounds of the expected cumulative reward and probabilistic bounded rewards based on existing results for imprecise Markov chains. These ideas are tested on a real case study involving the spend-down costs of geriatric medicine departments.

Cite this Paper

BibTeX
@InProceedings{pmlr-v147-termine21a, title = {Robust Model Checking with Imprecise Markov Reward Models}, author = {Termine, Alberto and Antonucci, Alessandro and Facchini, Alessandro and Primiero, Giuseppe}, booktitle = {Proceedings of the Twelveth International Symposium on Imprecise Probability: Theories and Applications}, pages = {299--309}, year = {2021}, editor = {Cano, Andrés and De Bock, Jasper and Miranda, Enrique and Moral, Serafı́n}, volume = {147}, series = {Proceedings of Machine Learning Research}, month = {06--09 Jul}, publisher = {PMLR}, pdf = {http://proceedings.mlr.press/v147/termine21a/termine21a.pdf}, url = {https://proceedings.mlr.press/v147/termine21a.html}, abstract = {In recent years probabilistic model checking has become an important area of research because of the diffusion of computational systems of stochastic nature. Despite its great success, standard probabilistic model checking suffers the limitation of requiring a sharp specification of the probabilities governing the model behaviour. The theory of imprecise probabilities offers a natural approach to overcome such limitation by a sensitivity analysis with respect to the values of these parameters. However, only extensions based on discrete-time imprecise Markov chains have been considered so far for such a robust approach to model checking. We present a further extension based on imprecise Markov reward models. In particular, we derive efficient algorithms to compute lower and upper bounds of the expected cumulative reward and probabilistic bounded rewards based on existing results for imprecise Markov chains. These ideas are tested on a real case study involving the spend-down costs of geriatric medicine departments.} }
Endnote
%0 Conference Paper %T Robust Model Checking with Imprecise Markov Reward Models %A Alberto Termine %A Alessandro Antonucci %A Alessandro Facchini %A Giuseppe Primiero %B Proceedings of the Twelveth International Symposium on Imprecise Probability: Theories and Applications %C Proceedings of Machine Learning Research %D 2021 %E Andrés Cano %E Jasper De Bock %E Enrique Miranda %E Serafı́n Moral %F pmlr-v147-termine21a %I PMLR %P 299--309 %U https://proceedings.mlr.press/v147/termine21a.html %V 147 %X In recent years probabilistic model checking has become an important area of research because of the diffusion of computational systems of stochastic nature. Despite its great success, standard probabilistic model checking suffers the limitation of requiring a sharp specification of the probabilities governing the model behaviour. The theory of imprecise probabilities offers a natural approach to overcome such limitation by a sensitivity analysis with respect to the values of these parameters. However, only extensions based on discrete-time imprecise Markov chains have been considered so far for such a robust approach to model checking. We present a further extension based on imprecise Markov reward models. In particular, we derive efficient algorithms to compute lower and upper bounds of the expected cumulative reward and probabilistic bounded rewards based on existing results for imprecise Markov chains. These ideas are tested on a real case study involving the spend-down costs of geriatric medicine departments.
APA
Termine, A., Antonucci, A., Facchini, A. & Primiero, G.. (2021). Robust Model Checking with Imprecise Markov Reward Models. Proceedings of the Twelveth International Symposium on Imprecise Probability: Theories and Applications, in Proceedings of Machine Learning Research 147:299-309 Available from https://proceedings.mlr.press/v147/termine21a.html.

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