  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.
