论文标题
基于电子价值的置信区间的选择后推断
Post-selection inference for e-value based confidence intervals
论文作者
论文摘要
假设可以为潜在兴趣的$ k $参数中的每一个构建有效的$（1-δ）$ - 置信区间（CI）。如果数据分析师使用任意数据依赖性标准选择某些子集$ s参数的参数，则由于选择偏差，因此所选参数的上述CI不再有效。我们设计了一种调整间隔的新方法，以控制错误的覆盖率（FCR）。主要建立的方法是Benjamini和Yekutieli的“按程序”（Jasa，2005年）。通过保证需要对选择标准和顺式依赖性的一定限制。我们提出了一种新的简单方法，相比之下，在原始顺式和任何（未知）选择标准之间的任何依赖性结构下都是有效的，但仅适用于我们称为e-cis的特殊但广泛的CI类。为了详细说明，我们的过程简单地报告了所选参数的$（1-δ| s |/k）$ - cis，我们证明它以$δ$控制fcr，以置于$δ$中，以隐式倒置电子价值；示例包括通过超级智能方法构建的示例，通过通用推理或Chernoff风格的边界等。 E-BY程序是可以接受的，并通过特定的校准器将逐个程序恢复为特殊情况。我们的工作也对顺序设置中的选择后推断有影响，因为它适用于停止时间，以连续监控置信序列以及在强盗采样下。我们使用数值模拟和来自Twitter的实际A/B测试数据证明了我们的过程的功效。
Suppose that one can construct a valid $(1-δ)$-confidence interval (CI) for each of $K$ parameters of potential interest. If a data analyst uses an arbitrary data-dependent criterion to select some subset $S$ of parameters, then the aforementioned CIs for the selected parameters are no longer valid due to selection bias. We design a new method to adjust the intervals in order to control the false coverage rate (FCR). The main established method is the "BY procedure" by Benjamini and Yekutieli (JASA, 2005). The BY guarantees require certain restrictions on the selection criterion and on the dependence between the CIs. We propose a new simple method which, in contrast, is valid under any dependence structure between the original CIs, and any (unknown) selection criterion, but which only applies to a special, yet broad, class of CIs that we call e-CIs. To elaborate, our procedure simply reports $(1-δ|S|/K)$-CIs for the selected parameters, and we prove that it controls the FCR at $δ$ for confidence intervals that implicitly invert e-values; examples include those constructed via supermartingale methods, via universal inference, or via Chernoff-style bounds, among others. The e-BY procedure is admissible, and recovers the BY procedure as a special case via a particular calibrator. Our work also has implications for post-selection inference in sequential settings, since it applies at stopping times, to continuously-monitored confidence sequences, and under bandit sampling. We demonstrate the efficacy of our procedure using numerical simulations and real A/B testing data from Twitter.
