使用鞅后验对反事实分布进行推断
Inference on counterfactual distributions using martingale posteriors
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中文总结 AI 辅助
研究通过估计完整反事实结果分布考虑后验效应分布，基于鞅后验框架提出推断方法，能灵活估计相关量且具稳健性和快速性，可用于多种分布及扩展，证明了收敛性并通过模拟和真实数据验证，如研究多种因素的影响。
中文摘要 AI 辅助
因果推断通常聚焦于平均效应，这可能掩盖效应分布的重要方面。本文通过估计完整的反事实结果分布来考虑整个后验效应分布。我们基于Fong等人（2023年）的鞅后验框架提出了一种反事实分布推断方法。该方法能灵活估计密度、分布函数及分位数等派生量，连贯量化目标估计量的认知不确定性。因其预测递归基于非参数模型，自然具有对参数假设的稳健性，实现速度通常也很快。此方法可应用于边际或条件反事实分布，还能扩展到工具变量设置。我们证明了鞅后验推断在反事实结果分布上的收敛性，并通过模拟和真实数据进行了说明，包括研究锌含片对普通感冒持续时间的影响、维生素A补充对儿童生存率的影响以及职业培训的效果等。
英文摘要
Causal inference is often focused on average effects, which can hide important aspects of the effect distributions. Here we consider the entire posterior effects distribution by estimating full counterfactual outcome distributions. We propose a methodology for inference on counterfactual distributions which builds upon the martingale posterior framework of Fong et al. (2023). This provides a highly flexible approach to estimating densities, distribution functions, and derived quantities such as quantiles, which coherently quantifies the epistemic uncertainty on any target estimand of interest. As the predictive recursions are based on an underlying nonparametric model (a Dirichlet process mixture model), our method naturally inherits robustness with respect to restrictive parametric assumptions. In addition, implementation of our method is typically very fast. This approach can be applied to marginal or conditional counterfactual distributions and is easily extended to an instrumental variables setup. Using the concept of almost conditionally identically distributed random variables, we prove convergence of the martingale posterior inference on the counterfactual outcome distributions for the causal models considered in the paper. We illustrate our approach on both simulated and real data. Using the latter, we investigate the effect of zinc lozenges on common cold duration, the impact of vitamin A supplementation on children's survival rates with one-sided non-compliance (analysed in Imbens and Rubin, 1997a) and the effect of job training (LaLonde, 1986).
