Abstract: Design-based inference, also known as randomization-based or finite-population inference, provides a principled framework for trustworthy statistical inference. It attributes randomness solely to the design mechanism, such as treatment assignment, survey sampling, or missingness, without imposing super-population distributional or modeling assumptions on the outcome data. From the seminal work of Fisher and Neyman to its recent resurgence, design-based inference has played a central role in causal inference, survey sampling, and missing data analysis. However, its use in many modern applications has been limited by a fundamental obstacle: existing design-based inference methods typically assume that propensity scores (i.e., design probabilities) are known, whereas in observational studies, real-world surveys, missing data problems, and many other settings, propensity scores are usually unknown and must be estimated from data. We propose propensity score propagation, a general framework for valid design-based inference with unknown propensity scores. The framework uses a regeneration-and-union procedure to propagate uncertainty from propensity score estimation into downstream design-based inference without introducing super-population assumptions about the outcomes. It accommodates both parametric and nonparametric propensity score estimation, supports flexible machine learning estimators, integrates seamlessly with existing design-based inference methods developed for settings with known propensity scores, and applies broadly across design-based problems. Theoretical and simulation results show that the proposed framework achieves nominal coverage, even when existing approaches exhibit substantial under-coverage.
About the Speaker: Siyu Heng, PhD is an Assistant Professor in the Department of Biostatistics, with an interest in both methodology and applied research. His areas of expertise are in causal inference, health data science, observational studies, randomized trials, sensitivity analysis, instrumental variables, measurement error, and in survey data and their applications in public health. Dr. Heng received his PhD in Applied Mathematics and Computational Science from the University of Pennsylvania.
