论文标题
比较二项式比例的置信区间与间隔得分
Comparing Confidence Intervals for a Binomial Proportion with the Interval Score
论文作者
论文摘要
超过55种不同的方法可以分别为二项式比例构建信心间隔（CI）。比较它们的方法对于确定应在实践中使用的方法。已建议间隔得分比较预测间隔。该分数是一个适当的评分规则，将覆盖范围结合在一起，以衡量校准和宽度作为清晰度的度量。我们根据预期的间隔评分评估了11个CI的二项式比例，并提出了一项摘要措施，该措施可以考虑到基本真实比例的不同权重。在统一的加权下，预期的间隔得分建议Wilson CI或贝叶斯可靠的间隔均匀。如果极低或高比例的重量更大，则分数建议基于Jeffreys的先验，建议贝叶斯可信间隔。虽然理论上需要更多的工作才能证明使用间隔得分进行CIS进行比较，但我们的结果表明，它构成了一种将覆盖范围和宽度相结合的有用方法。这种新颖的方法也可以在其他应用中使用。
There are over 55 different ways to construct a confidence respectively credible interval (CI) for the binomial proportion. Methods to compare them are necessary to decide which should be used in practice. The interval score has been suggested to compare prediction intervals. This score is a proper scoring rule that combines the coverage as a measure of calibration and the width as a measure of sharpness. We evaluate eleven CIs for the binomial proportion based on the expected interval score and propose a summary measure which can take into account different weighting of the underlying true proportion. Under uniform weighting, the expected interval score recommends the Wilson CI or Bayesian credible intervals with a uniform prior. If extremely low or high proportions receive more weight, the score recommends Bayesian credible intervals based on Jeffreys' prior. While more work is needed to theoretically justify the use of the interval score for the comparison of CIs, our results suggest that it constitutes a useful method to combine coverage and width in one measure. This novel approach could also be used in other applications.
