论文标题
具有成本效益的固定宽度置信区间，差异为两个伯努利比例的差异
Cost-Efficient Fixed-Width Confidence Intervals for the Difference of Two Bernoulli Proportions
论文作者
论文摘要
我们研究了两个Bernoulli分布的成功参数的差异，即$ P_X -P_Y $，如果目标是获得给定半宽的CI，而在两个分布之间的观察成本可能不同的情况下，则可以最大程度地减少给定半宽的CI。假设我们获得了成功参数的初步估计，我们提出了三种构建固定宽度顺式顺式的方法：（i）两阶段的采样过程，（ii）一种顺序进行批处理采样的顺序方法，以及（iii）$ \ ell $ stage $ stage'look-ahead”过程。我们使用Monte Carlo模拟表明，在不同的成功概率和观察成本方案下，我们提出的算法可节省大量成本，而不是基线（两阶段过程中最高50 \％），对于顺序方法，最高为15 \％）。此外，对于正在研究的场景，我们的顺序批次和$ \ ell $阶段的“ look-ahead”程序大约获得了标称覆盖范围，同时还满足了所需的宽度要求。从计算的角度来看，我们的顺序批次方法比“ look-aead”方法更有效，在所有情况下，平均运行时间至少更快的速度。
We study properties of confidence intervals (CIs) for the difference of two Bernoulli distributions' success parameters, $p_x - p_y$, in the case where the goal is to obtain a CI of a given half-width while minimizing sampling costs when the observation costs may be different between the two distributions. Assuming that we are provided with preliminary estimates of the success parameters, we propose three different methods for constructing fixed-width CIs: (i) a two-stage sampling procedure, (ii) a sequential method that carries out sampling in batches, and (iii) an $\ell$-stage "look-ahead" procedure. We use Monte Carlo simulation to show that, under diverse success probability and observation cost scenarios, our proposed algorithms obtain significant cost savings versus their baseline counterparts (up to 50\% for the two-stage procedure, up to 15\% for the sequential methods). Furthermore, for the battery of scenarios under study, our sequential-batches and $\ell$-stage "look-ahead" procedures approximately obtain the nominal coverage while also meeting the desired width requirement. Our sequential-batching method turned out to be more efficient than the "look-ahead" method from a computational standpoint, with average running times at least an order-of-magnitude faster over all the scenarios tested.
