A sequential hypothesis test based on a generalized Azuma inequality

Reijsbergen, Daniël; Scheinhardt, Willem R.W.; Boer, Pieter-Tjerk de

doi:10.1016/j.spl.2014.11.018

Cited by 3 publications

(5 citation statements)

References 8 publications

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“…Different hypothesis tests can be used, as discussed in [43]. In the following, we use the Azuma test [44] which guarantees predefined errors of first (false positive) and second (false negative) kind, even for small |𝑝 − 𝑝 𝔖 𝑐 m (Ψ, 𝑡)|. Potentially many SMC runs are required to obtain a result.…”

Section: Statistical Model Checkingmentioning

confidence: 99%

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Learning optimal decisions for stochastic hybrid systems

Niehage

Hartmanns

Remke

2021

Proceedings of the 19th ACM-IEEE International Conference on Formal Methods and Models for System Design

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We apply reinforcement learning to approximate the optimal probability that a stochastic hybrid system satisfies a temporal logic formula. We consider systems with (non)linear continuous dynamics, random events following general continuous probability distributions, and discrete nondeterministic choices. We present a discretized view of states to the learner, but simulate the continuous system. Once we have learned a near-optimal scheduler resolving the choices, we use statistical model checking to estimate its probability of satisfying the formula. We implemented the approach using Q-learning in the tools HYPEG and modes, which support Petri net-and hybrid automata-based models, respectively. Via two case studies, we show the feasibility of the approach, and compare its performance and effectiveness to existing analytical techniques for a linear model. We find that our new approach quickly finds near-optimal prophetic as well as non-prophetic schedulers, which maximize or minimize the probability that a specific signal temporal logic property is satisfied.

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Section: Statistical Model Checkingmentioning

confidence: 99%

“…Hypothesis testing. Table 3 presents the results of the Azuma [44] hypothesis test for the same number of training runs and discretization settings as in Table 2. The hypothesis checked is 𝑃 ≥0.73 (𝑡𝑡 𝑈 [0,11] (𝑥 tank ≥ 18)).…”

Section: The Linear Tankmentioning

confidence: 99%

Learning optimal decisions for stochastic hybrid systems

Niehage

Hartmanns

Remke

2021

Proceedings of the 19th ACM-IEEE International Conference on Formal Methods and Models for System Design

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“…Azuma Class-III test, with correctness guarantee based on the so-called generalized Azuma inequality [7].…”

Section: Test Classmentioning

confidence: 99%

Interactive comparison of hypothesis tests for statistical model checking

Boer

Reijsbergen

Scheinhardt

2016

Proceedings of the 9th EAI International Conference on Performance Evaluation Methodologies and Tools

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We present a web-based interactive comparison of hypothesis tests as are used in statistical model checking, providing users and tool developers with more insight into their characteristics. Parameters can be modified easily and their influence is visualized in real time; an integrated simulation engine further illustrates the behaviour of the tests. Finally, since the source code is available, it can serve as a framework in which newly developed tests can be tried.

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“…An informal argument is that the standard deviation of the process Z N grows proportionally to √ N , so that even under H 0 , given an infinite amount of time such boundaries will eventually be crossed with probability 1. This is discussed in greater detail in [29,30]. Also, u(N ) must grow slower than linearly in N , otherwise errors of the second kind will be too likely for small | p − p 0 |.…”

Section: Azuma Testmentioning

confidence: 99%

“…For this case, both the correctness of the test and a lower bound on the power are proven in [29,30] using a bounding result that is comparable to, and inspired by, Ross' "generalized Azuma inequality" in Sect. 6.5 of [32] (which also explains the name of the test).…”

Section: Azuma Testmentioning

confidence: 99%

On hypothesis testing for statistical model checking

Reijsbergen

Boer

Scheinhardt

et al. 2014

Int J Softw Tools Technol Transfer

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Hypothesis testing is an important part of statistical model checking (SMC). It is typically used to verify statements of the form p > p 0 or p < p 0 , where p is an unknown probability intrinsic to the system model and p 0 is a given threshold value. Many techniques for this have been introduced in the SMC literature. We give a comprehensive overview and comparison of these techniques, starting by introducing a framework in which they can all be described. We distinguish between three classes of techniques, differing in what type of output correctness guarantees they give when the true p is very close to the threshold p 0 . For each technique, we show how to parametrise it in terms of quantities that are meaningful to the user. Having parametrised them consistently, we graphically compare the boundaries of their decision thresholds, and numerically compare the correctness, power and efficiency of the tests. A companion website allows users to get more insight in the properties of the tests by interactively manipulating the parameters.

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A sequential hypothesis test based on a generalized Azuma inequality

Abstract: We present a new power-one sequential hypothesis test based on a bound for the probability that a bounded zero-mean martingale ever crosses a curve of the form a(n + k) b . The proof of the bound is of independent interest.

Cited by 3 publications

References 8 publications

Learning optimal decisions for stochastic hybrid systems

Learning optimal decisions for stochastic hybrid systems

Interactive comparison of hypothesis tests for statistical model checking

On hypothesis testing for statistical model checking

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