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The Role of Informative Priors in Zero-Numerator Problems: Being Conservative versus Being Candid

Robert L. Winkler, James E. Smith and Dennis G. Fryback
The American Statistician
Vol. 56, No. 1 (Feb., 2002), pp. 1-4
Stable URL: http://www.jstor.org/stable/3087320
Page Count: 4
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The Role of Informative Priors in Zero-Numerator Problems: Being Conservative versus Being Candid
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Abstract

The "Rule of Three" gives an approximation for an upper 95% confidence bound for a proportion in a zero-numerator problem, which occurs when the observed relative frequency is zero. We compare the results from the Rule of Three with those from a Bayesian approach with noninformative and informative priors. Informative priors are especially valuable in zero-numerator problems because they can represent the available information and because different noninformative priors can give conflicting advice. Moreover, the use of upper 95% bounds and noninformative priors in an effort to be conservative may backfire when the values are used in further predictive or decision-theoretic calculations. It is better to be candid than conservative, using all of the information available in forming the prior and considering the uncertainty represented by the full posterior distribution.

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