General Bayesian inference for causal effects using covariate balancing procedure

In observational studies, the propensity score plays a central role in estimating causal effects of interest. The inverse probability weighting (IPW) estimator is commonly used for this purpose. 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. However, these methods require considering parameters that dominate the uncertainty of sampling and treatment allocation. This study proposes a novel Bayesian estimating procedure that necessitates probabilistically deciding the parameter, rather than deterministically. Since the IPW estimator and propensity score estimator can be derived as solutions to certain loss functions, the general Bayesian paradigm, which does not require the considering the full likelihood, can be applied. Therefore, our proposed method only requires the same level of assumptions as ordinary causal inference contexts. The proposed Bayesian method demonstrates equal or superior results compared to some previous methods in simulation experimentss, and is also applied to real data, namely the Whitehall dataset.