### Abstract

One of the main applications of probabilistic model checking is to decide whether the probability of a property of interest is above or below a threshold. Using statistical model checking (SMC), this is done using a combination of stochastic simulation and statistical hypothesis testing. When the probability of interest is very small, one may need to resort to rare-event simulation techniques, in particular importance sampling (IS). However, IS simulation does not yield 0/1-outcomes, as assumed by the hypothesis tests commonly used in SMC, but likelihood ratios that are typically close to zero, but which may also take large values.
In this paper we consider two possible ways of combining IS and SMC. One involves a classical IS-scheme from the rare-event simulation literature that yields likelihood ratios with bounded support when applied to a certain (nontrivial) class of models. The other involves a particular hypothesis testing scheme that does not require a-priori knowledge about the samples, only that their variance is estimated well.

Original language | English |
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Title of host publication | Leveraging Applications of Formal Methods, Verification and Validation: Foundational Techniques |

Subtitle of host publication | 7th International Symposium, ISoLA 2016, Imperial, Corfu, Greece, October 10–14, 2016, Proceedings, Part I |

Editors | Tiziana Margaria, Bernhard Steffen |

Publisher | Springer |

Pages | 16-26 |

Number of pages | 11 |

ISBN (Electronic) | 978-3-319-47166-2 |

ISBN (Print) | 978-3-319-47165-5 |

DOIs | |

Publication status | Published - 10 Oct 2016 |

Event | 7th International Symposium on Leveraging Applications of Formal Methods, Verification and Validation, ISoLA 2016 - Corfu, Greece Duration: 10 Oct 2016 → 14 Oct 2016 Conference number: 7 http://www.isola-conference.org/isola2016/ |

### Publication series

Name | Lecture Notes in Computer Science |
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Publisher | Springer |

Volume | 9952 |

ISSN (Print) | 0302-9743 |

ISSN (Electronic) | 1611-3349 |

### Conference

Conference | 7th International Symposium on Leveraging Applications of Formal Methods, Verification and Validation, ISoLA 2016 |
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Abbreviated title | ISoLA 2016 |

Country | Greece |

City | Corfu |

Period | 10/10/16 → 14/10/16 |

Internet address |

### Keywords

- IR-103348
- EC Grant Agreement nr.: FP7/318490
- METIS-321693
- EC Grant Agreement nr.: FP7/600708
- EWI-27678

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## Cite this

Reijsbergen, D. P., de Boer, P-T., & Scheinhardt, W. R. W. (2016). Hypothesis testing for rare-event simulation: limitations and possibilities. In T. Margaria, & B. Steffen (Eds.),

*Leveraging Applications of Formal Methods, Verification and Validation: Foundational Techniques: 7th International Symposium, ISoLA 2016, Imperial, Corfu, Greece, October 10–14, 2016, Proceedings, Part I*(pp. 16-26). (Lecture Notes in Computer Science; Vol. 9952). Springer. https://doi.org/10.1007/978-3-319-47166-2_2