Posterior Predictive Propensity Scores and $p$-Values
后验预测倾向得分与 p 值AI 解读 ↓
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AI 根据所提供的论文材料归类：摘要明确讨论观察性研究中的倾向得分、因果效应零假设与双重稳健检验，属于因果推断。
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后验预测倾向得分与 p 值
- 研究问题
- 如何在贝叶斯观察性因果分析中纳入倾向得分，并构造兼顾强零假设、平均效应弱零假设与频率学性质的检验？
- 方法与思路
- 作者对倾向得分的后验预测分布平均 Fisher 随机化检验的 p 值，并使用学生化双重稳健估计量作为检验统计量。
- 材料陈述的贡献
- 摘要称，该检验继承双重稳健性质，对零平均效应的弱零假设渐近有效，并可能在极端倾向得分下改善有限样本表现。
- 阅读关注点
- 应核对强零假设与弱零假设的不同论证、后验预测分布构造、双重稳健条件，以及有限样本比较采用的模型与基准。
- 阅读边界
- 这是 arXiv 预印本，同行评审及期刊接收未核实；摘要未列出完整正则条件或性能数值，所述有限样本改善具有情境限制。
原文摘要
\citet{Rosenbaum83ps} introduced the notion of the propensity score and discussed its central role in causal inference with observational studies. Their paper, however, caused a fundamental incoherence with an early paper by \citet{Rubin78}, which showed that the propensity score does not play any role in the Bayesian analysis of unconfounded observational studies if the priors on the propensity score and outcome models are independent. Despite the serious efforts made in the literature, it is generally difficult to reconcile these contradicting results. We offer a simple approach to incorporating the propensity score in Bayesian causal inference based on the posterior predictive $p$-value. To motivate a simple procedure, we focus on the model with the strong null hypothesis of no causal effects for any units whatsoever. Computationally, the proposed posterior predictive $p$-value equals the classic $p$-value based on the Fisher randomization test averaged over the posterior predictive distribution of the propensity score. Moreover, using the studentized doubly robust estimator as the test statistic, the proposed $p$-value inherits the doubly robust property and is also asymptotically valid for testing the weak null hypothesis of zero average causal effect. Perhaps surprisingly, this Bayesianly motivated $p$-value can have better frequentist's finite-sample performance than the frequentist's $p$-value based on the asymptotic approximation especially when the propensity scores can take extreme values.