The Role of Informative Priors in Zero-Numerator Problems
The Role of Informative Priors in Zero-Numerator Problems
复制标题
信息先验在零分子问题中的作用
DOI：
10.1198/000313002753631295
复制
发表时间：
2002
期刊：
影响因子：
--
通讯作者：
D. Fryback
中科院分区：
文献类型：
--
作者：
R. L. Winkler;James E. Smith;D. Fryback
“三法则”给出了零分子问题中某个比例的 95% 置信上限的近似值，这种情况发生在观察到的相对频率为零时。我们将三法则的结果与具有非信息性和信息性先验的贝叶斯方法的结果进行比较。信息先验在零分子问题中特别有价值，因为它们可以代表可用的信息，并且因为不同的非信息先验可以给出相互矛盾的建议。此外，当这些值用于进一步的预测或决策理论计算时，为了保守而使用 95% 上限和无信息先验可能会适得其反。坦诚比保守要好，使用所有可用的信息来形成先验并考虑完整后验分布所代表的不确定性。
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 conicting 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.