The Rubin Causal Model (RCM), also called Potential Outcome Framework, assumes any unit in a population has potential outcomes under any treatment relevant in a study. For example $Y_1$ denotes the outcome under treatment, $Y_0$ the outcome under control. In a non-randomized experiment the fact that in expectation the quantity
$$E(Y_1|T=1) - E(Y_0|T=0)$$
is observed in expectation as the mean difference between treated and untreated units, where $T$ denotes the treatment assignment, causes selection bias against the average treatment effect
The key problem is that part of the data needed for causal inference is unobserved, in particular $E(Y_1|T=0)$ and $E(Y_0|T=1)$. There are several approaches to inference about this treatment effect, prominently weighting, stratification, or some other form of matching on the propensity score.
An alternative approach tries to estimate the unobserved potential outcome distributions $P(Y_1,Y_0)$ directly using Bayesian techniques, such as multiple imputation. What are key papers that attempt causal inference by solving the missing data problem by multiple imputation or other Bayesian techniques?