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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 "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.
The American Statistician © 2002 American Statistical Association