随机干预效应的校准贝叶斯推断
Calibrated Bayesian Inference for Stochastic Intervention Effects
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中文总结 AI 辅助
本研究针对随机干预效应的贝叶斯推断，提出一种不改变先验或拟合算法的后处理校正方法，经理论与模拟验证可提升推断的校准度与性能，并通过他汀类药物对LDL胆固醇影响的实例说明其应用。
中文摘要 AI 辅助
因果推断正从确定性处理分配定义的经典因果效应（如平均处理效应）不断扩展至随机干预效应，后者可弱化正性要求并具备更强的政策相关性。非参数贝叶斯模型因灵活性及固有不确定性传播特性，适合估计此类效应，但针对目标因果效应的后验不确定性未必经过良好校准。我们提出一种简单的后处理校正方法，可应用于后验样本而不改变先验或拟合算法。我们证明，针对一大类随机干预，校正后的后验能产生渐近有效推断及具有渐近有效频率覆盖的可信区间，形式上满足半参数伯恩斯坦-冯·米塞斯定理。该理论涵盖独立于观测处理过程指定的干预，以及修改该过程的干预，包括增量倾向评分干预和新的幂倾斜干预。核心贡献是提出SoftBART的新理论，包括该灵活树状贝叶斯模型支持随机干预效应校准贝叶斯推断的条件。模拟结果显示，与未校正的贝叶斯分析相比，该校正可降低偏差并提升覆盖度，同时仍与频率论替代方法具有竞争力。我们通过估算在假设的他汀类药物治疗接受几率增减情况下，预期低密度脂蛋白（LDL）胆固醇的变化来例证该方法。
英文摘要
Causal inference increasingly extends beyond classical causal effects defined by deterministic treatment assignments, such as the average treatment effect, to stochastic intervention effects that can weaken positivity requirements and offer greater policy relevance. Nonparametric Bayesian models are attractive for estimating these effects due to their flexibility and inherent uncertainty propagation, but this posterior uncertainty need not be well calibrated for the causal effect of interest. We develop a simple post-processing correction that can be applied to posterior samples without changing the prior or fitting algorithm. We prove that, for a broad class of stochastic interventions, the corrected posterior yields asymptotically efficient inference and credible intervals with asymptotically valid frequentist coverage; formally, it satisfies a semiparametric Bernstein-von Mises theorem. The theory covers interventions specified independently of the observed treatment process, as well as interventions that modify it, including incremental propensity score interventions and a new power-tilt intervention. A central contribution is new theory for SoftBART, including conditions under which this flexible tree-based Bayesian model supports calibrated Bayesian inference for stochastic intervention effects. In simulations, the correction reduces bias and improves coverage relative to the uncorrected Bayesian analysis while remaining competitive with frequentist alternatives. We illustrate the method by estimating how expected LDL cholesterol would change under hypothetical increases or decreases in the odds of receiving statin therapy.
