We develop and analyze empirical Bayes Stein-type estimators for use in the
estimation of causal effects in large-scale online experiments. While online
experiments are generally thought to be distinguished by their large sample
size, we focus on the multiplicity of treatment groups. The typical analysis
practice is to use simple differences-in-means (perhaps with covariate
adjustment) as if all treatment arms were independent. In this work we develop
consistent, small bias, shrinkage estimators for this setting. In addition to
achieving lower mean squared error these estimators retain important
frequentist properties such as coverage under most reasonable scenarios. Modern
sequential methods of experimentation and optimization such as multi-armed
bandit optimization (where treatment allocations adapt over time to prior
responses) benefit from the use of our shrinkage estimators. Exploration under
empirical Bayes focuses more efficiently on near-optimal arms, improving the
resulting decisions made under uncertainty. We demonstrate these properties by
examining seventeen large-scale experiments conducted on Facebook from April to
June 2017.

本研究开发并分析了经验贝叶斯斯坦型估计量，用于在大规模在线实验中估计因果效应。我们通过对 Facebook 在 2017 年 4 月至 6 月进行的 17 个大规模实验的研究来展示这些性质。