Accurate confidence intervals for binomial proportion and Poisson rate estimation.
Citations
377 citations
Cites background from "Accurate confidence intervals for b..."
...As explained eloquently by both Kraft et al. (1991) and Ross (2003), there is a fundamental difference between the ‘classical’ and ‘Bayesian’ definitions of the term ‘confidence interval’....
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...…¼ k=n, for a given value of p is, of course, proportional to pkqn–k. Normalisation of this likelihood function over 0, p, 1 defines a ‘beta distribution’ with integer parameters a¼ kþ 1 and b¼ n kþ 1: Bða; bÞ ¼ ðaþ b 1Þ!ða 1Þ!ðb 1Þ! p a 1qb 1 ð2Þ where q¼ 1 p (e.g., Gelman et al. 2003; Ross 2003)....
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220 citations
Cites methods from "Accurate confidence intervals for b..."
...In this case, there exist specific confidence interval constructions that can replace the one obtained by using the central limit theorem (see for instance [7], typical examples being...
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219 citations
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References
4,095 citations
"Accurate confidence intervals for b..." refers methods in this paper
...6 is the error plot for method 5 (Clopper–Pearson)....
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...Method 5, Clopper–Pearson CIs: Method 5 is based on Clopper and Pearson [11]....
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...The implementations of method 5 (Clopper–Pearson based) and method 6 (Normal approximation based) are those of [13] for proportion di erences....
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...The di erence CIEs (prop−di −ci and rate−di −ci) are much slower, taking tens of seconds in some cases, and the comparison with the Normal and Clopper–Pearson methods is limited to the results reported in [13]....
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...The CIEs’ accuracies are reported based on a Monte Carlo validated integration of the posterior probability distribution and compared to the normal approximation and Clopper–Pearson methods....
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"Accurate confidence intervals for b..." refers methods in this paper
...An alternative Clopper–Pearson method [4] is also well known....
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351 citations
"Accurate confidence intervals for b..." refers background in this paper
...From the “classical” or sampling theory perspective [2], there is some unknown, but “true” xed value of the estimated parameter....
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