We develop a new approach for quantifying uncertainty in finite populations, by using design distributions to calibrate sensitivity parameters in finite population identified sets. This yields uncertainty intervals that can be interpreted as identified sets, robust Bayesian credible sets, or uniform frequentist design-based confidence sets. We focus on quantifying uncertainty about the average treatment effect, where our approach (1) yields design-based confidence intervals which allow for heterogeneous treatment effects without using asymptotics, (2) provides a new motivation for examining covariate balance, and (3) gives a new formal analysis of the role of randomization. We illustrate our approach in three empirical applications.

翻译：我们开发了一种量化有限总体中不确定性的新方法，其核心是利用设计分布来校准有限总体识别集中的敏感性参数。由此产生的不确定区间可被解释为识别集、稳健贝叶斯可信集或统一频率学派基于设计的置信集。我们聚焦于平均处理效应的量化不确定性，该方法能够：(1) 在不依赖渐近理论的情况下，构建允许处理效应异质性的基于设计的置信区间；(2) 为检验协变量平衡提供新的动机；(3) 对随机化的作用给出新的形式化分析。我们通过三项实证应用展示了该方法。