On finite-population Bayesian inferences for $2^K$ factorial designs with binary outcomes

Abstract: Inspired by the pioneering work of Rubin (1978), we employ the potential outcomes framework to develop a finite-population Bayesian causal inference framework for randomized controlled $2^K$ factorial designs with binary outcomes, which are common in medical research. As demonstrated by simulated and empirical examples, the proposed framework corrects the well-known variance over-estimation issue of the classic "Neymanian" inference framework, under various settings.