计算分组泄漏总和的置信区间
Calculating a confidence interval on the sum of binned leakage
摘要：
计算错误分类结果的预期数量是罕见事件搜索特别感兴趣的标准问题。Clopper-Pearson方法允许计算错误分类量的经典置信区间，如果数据都来自相同的二项概率分布。然而，数据通常通过将其分解为几个箱来更好地描述，每个箱由不同的二项分布表示。我们描述并提供了一种算法，用于计算一个经典的置信区间的预期总数量的误分类事件从几个箱子，校准数据的基础上，具有相同的概率误分类的一个bin由bin的基础上。我们的方法避免了计算密集的多维搜索，通过引入拉格朗日乘子和执行标准的根查找。该方法的时间复杂度仅为箱数的二次方，并且产生的置信区间仅略微保守。
英文摘要：
Calculating the expected number of misclassified outcomes is a standard problem of particular interest for rare-event searches. The Clopper-Pearson method allows calculation of classical confidence intervals on the amount of misclassification if data are all drawn from the same binomial probability distribution. However, data is often better described by breaking it up into several bins, each represented by a different binomial distribution. We describe and provide an algorithm for calculating a classical confidence interval on the expected total number of misclassified events from several bins, based on calibration data with the same probability of misclassification on a bin-by-bin basis. Our method avoids a computationally intensive multidimensional search by introducing a Lagrange multiplier and performing standard root finding. This method has only quadratic time complexity as the number of bins, and produces confidence intervals that are only slightly conservative.
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