Design-based inference, also known as randomization-based or finite-population inference, provides a principled framework for trustworthy statistical inference by attributing randomness solely to the design mechanism (e.g., treatment assignment, survey sampling, or missingness), without imposing super-population distributional or modeling assumptions on outcome data. From Fisher's and Neyman's seminal work to the recent resurgence of design-based inference, this perspective has played a central role in causal inference, survey sampling, and missing data analysis. However, a fundamental obstacle has limited its use in many modern applications: existing design-based inference theory typically relies on known propensity scores (i.e., known design probabilities), whereas propensity scores are usually unknown in observational studies, real-world survey settings, and missing data problems. We propose propensity score propagation, a general framework for valid design-based inference with unknown propensity scores. The framework introduces a regeneration-and-union procedure that propagates uncertainty from propensity score estimation into downstream design-based inference without imposing super-population outcome assumptions. It accommodates both parametric and nonparametric propensity score models, integrates seamlessly with existing design-based methods developed under known propensity scores, and applies broadly across design-based inference problems. Theoretical results and simulation studies show that the proposed framework achieves nominal coverage, even when existing approaches exhibit substantial under-coverage.

翻译：基于设计的推断（又称随机化推断或有限总体推断）通过将随机性完全归因于设计机制（如处理分配、调查抽样或数据缺失），在不依赖超总体分布假设或结果数据建模假设的前提下，为可信统计推断提供了严谨框架。从费希尔和内曼的奠基性工作到近期基于设计推断的复兴，该视角在因果推断、抽样调查和缺失数据分析中始终占据核心地位。然而，一个根本性障碍限制了其在现代应用中的广泛使用：现有基于设计的推断理论通常依赖已知倾向性得分（即已知的设计概率），而在观察性研究、真实调查场景和缺失数据问题中，倾向性得分往往未知。我们提出倾向性得分传播这一通用框架，用于在倾向性得分未知时实现有效的基于设计推断。该框架引入了再生-联合过程，将倾向性得分估计的不确定性传播至下游基于设计的推断，而无需依赖超总体结果假设。它兼容参数与非参数倾向性得分模型，可与现有已知倾向性得分下的基于设计方法无缝集成，并广泛适用于各类基于设计的推断问题。理论结果与仿真研究表明，即使现有方法出现显著覆盖不足，本框架仍能达到名义覆盖水平。