Publications [#278469] of Robert L. Winkler
Papers Published
- Winkler, RL; Smith, JE; Fryback, DG. "The role of informative priors in zero-numerator problems: Being conservative versus being candid." American Statistician 56.1 (January, 2002): 1-4. [doi]
(last updated on 2026/01/17)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.