论文标题
无需替代的采样的置信序列
Confidence sequences for sampling without replacement
论文作者
论文摘要
许多实用任务涉及依次取得依次的取样（wor），从有限的$ n $中进行替换（wor），以估算一些参数$θ^\ star $。准确地量化整个过程中的不确定性是一项非平凡的任务，但这是必要的，因为它通常决定我们何时停止收集样品并自信地报告结果。我们提供了一套用于设计置信序列（CS）的工具，以$θ^\ star $。 CS是一系列置信度设置$（C_N）_ {n = 1}^n $，大小收缩，并且全部包含$θ^\ star $同时具有高概率。我们提出了一种使用贝叶斯工具来构建常见的CS的通用方法，这是基于以下事实：地面真相的后验是一个the脚。然后，我们向抽样的hoeffding-和经验伯恩斯坦型的时间均匀的CSS和固定的时间置信区间介绍，这会改善文献中以前的界限，并明确量化了Wor采样的好处。
Many practical tasks involve sampling sequentially without replacement (WoR) from a finite population of size $N$, in an attempt to estimate some parameter $θ^\star$. Accurately quantifying uncertainty throughout this process is a nontrivial task, but is necessary because it often determines when we stop collecting samples and confidently report a result. We present a suite of tools for designing confidence sequences (CS) for $θ^\star$. A CS is a sequence of confidence sets $(C_n)_{n=1}^N$, that shrink in size, and all contain $θ^\star$ simultaneously with high probability. We present a generic approach to constructing a frequentist CS using Bayesian tools, based on the fact that the ratio of a prior to the posterior at the ground truth is a martingale. We then present Hoeffding- and empirical-Bernstein-type time-uniform CSs and fixed-time confidence intervals for sampling WoR, which improve on previous bounds in the literature and explicitly quantify the benefit of WoR sampling.
