A Bayesian view of doubly robust causal inference: Table 1.
本文从贝叶斯角度解释为何双重稳健推断无法基于纯似然方法，并提出一种结合逆概率加权的贝叶斯后验预测方法来实现双重稳健估计。
In causal inference the effect of confounding may be controlled using regression adjustment in an outcome model, propensity score adjustment, inverse probability of treatment weighting or a combination of these. Approaches based on modelling the treatment assignment mechanism, along with their doubly robust extensions, have been difficult to motivate using formal likelihood-based or Bayesian arguments, as the treatment assignment model plays no part in inferences concerning the expected outcomes. On the other hand, forcing dependency between the outcome and treatment assignment models by allowing the former to be misspecified results in loss of the balancing property of the propensity scores and the loss of any double robustness. In this paper, we explain in the framework of misspecified models why doubly robust inferences cannot arise from purely likelihood-based arguments. As an alternative to Bayesian propensity score analysis, we propose a Bayesian posterior predictive method for constructing doubly robust estimation procedures by incorporating the inverse treatment assignment probabilities as importance sampling weights in Monte Carlo integration.