Fixed-Width Sequential Confidence Intervals for a Proportion

Frey, Jesse

doi:10.1198/tast.2010.09140

Cited by 30 publications

(24 citation statements)

References 23 publications

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“…Therefore, it is not prohibitively expensive to get a very high degree of confidence even on the models which are prohibitively difficult to solve analytically. In practice, we can exploit the fact that our samples follow binomial distribution and hence the probability estimation is even more efficient by using sequential methods [26], which adapt to the actual probability value and the confidence interval is computed by more precise methods [17].…”

Section: Pr[<=n](<> Expr)mentioning

confidence: 99%

Statistical and exact schedulability analysis of hierarchical scheduling systems

Boudjadar

David

Kim

et al. 2016

Science of Computer Programming

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This paper contains two contributions: 1) A development methodology involving two techniques to enhance the resource utilization and 2) a new generic multi-core resource model for hierarchical scheduling systems. As the first contribution, we propose a two-stage development methodology relying on the adjustment of timing attributes in the detailed models during the design stage. We use a lightweight method (statistical model checking) for design exploration, easily assuring high confidence in the correctness of the models. Once a satisfactory design has been found, it can be proved schedulable using the computation costly method (symbolic model checking). In order to analyze a hierarchical scheduling system compositionally, we introduce the notion of a stochastic supplier modeling the supply of resources from each component to its child components in the hierarchy. We specifically investigate two different techniques to widen the set of provably schedulable systems: 1) a new supplier model; 2) restricting the potential task offsets. We also provide a way to estimate the minimum resource supply (budget) that a component is required to provide. In contrast to analytical methods, we prove nonschedulable cases via concrete counterexamples. By having richer and more detailed scheduling models this framework, has the potential to prove the schedulability of more systems. As the second contribution, we introduce a generic resource model for multi-core hierarchical scheduling systems, and show how it can be instantiated for classical resource models: Periodic Resource Models (PRM) and Explicit Deadline Periodic (EDP) resource models. The generic multi-core resource model is presented in the context of a compositional model-based approach for schedulability analysis of hierarchical scheduling systems. The multi-core framework presented in this paper is an extension of the single-core framework used for the analysis in the rest of the paper.

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Section: Pr[<=n](<> Expr)mentioning

confidence: 99%

Statistical and exact schedulability analysis of hierarchical scheduling systems

Boudjadar

David

Kim

et al. 2016

Science of Computer Programming

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“…The first was proposed by Frey in [20] and the second, the Conditional Method, was proposed in our earlier work in [26]. Frey's method uses a modified Wald-type sequential confidence interval based on the stopping time…”

Section: Comparisonsmentioning

confidence: 99%

“…The sequential version of the interval estimation aims exactly at reducing the sample size by selecting it to be random and, in particular, a stopping time controlled by the observations themselves. The literature focusing on the sequential setup of the problem is limited compared to its fixed sample-size counterpart (see [18]- [20]). However, none of these articles is able to claim optimality of their corresponding schemes in any sense.…”

Section: Introductionmentioning

confidence: 99%

Optimal Stopping for Interval Estimation in Bernoulli Trials

Yaacoub

Moustakides

Mei

2019

IEEE Trans. Inform. Theory

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We propose an optimal sequential methodology for obtaining confidence intervals for a binomial proportion θ. Assuming that an i.i.d. random sequence of Benoulli(θ) trials is observed sequentially, we are interested in designing a) a stopping time T that will decide when is the best time to stop sampling the process, and b) an optimum estimatorθ T that will provide the optimum center of the interval estimate of θ. We follow a semi-Bayesian approach, where we assume that there exists a prior distribution for θ, and our goal is to minimize the average number of samples while we guarantee a minimal coverage probability level. The solution is obtained by applying standard optimal stopping theory and computing the optimum pair (T,θ T ) numerically. Regarding the optimum stopping time component T , we demonstrate that it enjoys certain very uncommon characteristics not encountered in solutions of other classical optimal stopping problems. Finally, we compare our method with the optimum fixed-sample-size procedure but also with existing alternative sequential schemes.

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“…The method was also used by Schultz et al (1973) for computing sequential binomial probabilities for multistage procedures used in drug screening. Similar path-count approaches for binomial settings were detailed in Franzen (2001) and Frey (2010) to obtain fixed width confidence intervals on π with exact confidence level. It is significant to note that all of these previous works consider only the binomial case, that is, where sampling is performed with replacement, or from a lot of infinite size.…”

Section: Introductionmentioning

confidence: 99%

Closed Sequential and Multistage Inference on Binary Responses With or Without Replacement

Ignatova

Deutsch

Edwards

2012

The American Statistician

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We consider closed sequential or multistage sampling, with or without replacement, from a lot of N items, where each item can be identified as defective (in error, tainted, etc.) or not. The goal is to make inference on the proportion, π , of defectives in the lot, or equivalently on the number of defectives in the lot D = Nπ. It is shown that exact inference on π using closed (bounded) sequential or multistage procedures with general prespecified elimination boundaries is completely tractable and not at all inconvenient using modern statistical software. We give relevant theory and demonstrate functions for this purpose written in R (R Development Core Team 2005, available as online supplementary material). Applicability of the methodology is illustrated in three examples: (1) sharpening of Wald's (1947) sequential probability ratio test used in industrial acceptance sampling, (2) two-stage sampling for auditing Medicare or Medicaid health care providers, and (3) risk-limited sequential procedures for election audits.

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Fixed-Width Sequential Confidence Intervals for a Proportion

Cited by 30 publications

References 23 publications

Statistical and exact schedulability analysis of hierarchical scheduling systems

Statistical and exact schedulability analysis of hierarchical scheduling systems

Optimal Stopping for Interval Estimation in Bernoulli Trials

Closed Sequential and Multistage Inference on Binary Responses With or Without Replacement

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