  In observational studies, the propensity score plays a central role in
estimating causal effects of interest. The inverse probability weighting (IPW)
estimator is especially commonly used. However, if the propensity score model
is misspecified, the IPW estimator may produce biased estimates of causal
effects. Previous studies have proposed some robust propensity score estimation
procedures; these methods, however, require consideration of parameters that
dominate the uncertainty of sampling and treatment allocation. In this
manuscript, we propose a novel Bayesian estimating procedure that necessitates
deciding the parameter probability, rather than deterministically. Since both
the IPW estimator and the propensity score estimator can be derived as
solutions to certain loss functions, the general Bayesian paradigm, which does
not require the consideration of the full likelihood, can be applied. In this
sense, our proposed method only requires the same level of assumptions as
ordinary causal inference contexts.
