论文标题
多项式计数数据的任何时间录音推断
Anytime-Valid Inference for Multinomial Count Data
论文作者
论文摘要
许多实验涉及治疗组之间计数的比较。示例包括转化率实验中成功的注册数量，或金丝雀实验中软件版本产生的错误数量。观察结果通常到达数据流和从业者希望不断监视其实验，顺序测试假设，同时在可选停止和延续下保持I型错误概率。这些目标在实践中经常通过非平稳时间动态变得复杂。我们通过对多项式假设的顺序检验，关于许多不均匀的Bernoulli过程的假设以及许多关于许多时间固定的泊松计数过程的假设来提供实用的解决方案。为了进行估计，我们进一步提供了多项式概率向量的置信序列，这在不均匀的Bernoulli过程的概率之间都是对比度，以及在时间均匀的泊松计数过程的强度之间的所有对比。这些共同为各种涉及计数结果的实验提供了一个“随时随地的”推理框架，我们为许多行业应用说明了这一点。
Many experiments are concerned with the comparison of counts between treatment groups. Examples include the number of successful signups in conversion rate experiments, or the number of errors produced by software versions in canary experiments. Observations typically arrive in data streams and practitioners wish to continuously monitor their experiments, sequentially testing hypotheses while maintaining Type I error probabilities under optional stopping and continuation. These goals are frequently complicated in practice by non-stationary time dynamics. We provide practical solutions through sequential tests of multinomial hypotheses, hypotheses about many inhomogeneous Bernoulli processes and hypotheses about many time-inhomogeneous Poisson counting processes. For estimation, we further provide confidence sequences for multinomial probability vectors, all contrasts among probabilities of inhomogeneous Bernoulli processes and all contrasts among intensities of time-inhomogeneous Poisson counting processes. Together, these provide an "anytime-valid" inference framework for a wide variety of experiments dealing with count outcomes, which we illustrate with a number of industry applications.
