It is not always clear how to adjust for control data in causal inference, balancing the goals of reducing bias and variance. We show how, in a setting with repeated experiments, Bayesian hierarchical modeling yields an adaptive procedure that uses the data to determine how much adjustment to perform. The result is a novel analysis with increased statistical efficiency compared with the default analysis based on difference estimates. We demonstrate this procedure on two real examples, as well as on a series of simulated datasets. We show that the increased efficiency can have real-world consequences in terms of the conclusions that can be drawn from the experiments. We also discuss the relevance of this work to causal inference and statistical design and analysis more generally.

中文翻译：

---

Slaming the sham：用于噪声控制数据自适应调整的贝叶斯模型

如何在因果推断中调整控制数据，平衡减少偏差和方差的目标并不总是很清楚。我们展示了在重复实验的环境中，贝叶斯分层建模如何产生一个自适应程序，该程序使用数据来确定要执行多少调整。结果是一种新颖的分析，与基于差异估计的默认分析相比，具有更高的统计效率。我们在两个真实示例以及一系列模拟数据集上演示了此过程。我们表明，就可以从实验中得出的结论而言，提高的效率可能会对现实世界产生影响。我们还更广泛地讨论了这项工作与因果推断以及统计设计和分析的相关性。