Bayesian causal estimation via model misspecification

随着越来越多的观测数据变得可用，迫切需要使用适当的统计模型来回答有意义的因果问题。因果推理在所有科学中都得到了广泛的研究，例如公共交通和流行病学。推理目标是一个因果被估量，它衡量不同干预措施下研究单元的预期结果的变化。它在频率主义半参数理论中有着良好的基础，通常通过结果回归和倾向评分调整来估计因果参数。贝叶斯对应，但是，是不明显的双重稳健估计涉及一个半参数的制定在没有一个完全指定的似然函数。在这个项目中，我们的目标是研究从标准的先验到后验更新中进行贝叶斯因果推理的解决方案，不需要观察值的参数族，并且对模型误指定也具有鲁棒性。我们将应用所提出的方法来评估和量化伦敦的停止和搜索在过去十年中威慑毒品犯罪的因果关系的影响。

With an increasing amount of observational data becoming available, there is a pressing need to use appropriate statistical models to answer meaningful causal questions. Causal inference is widely studied across all sciences, such as public transportation and epidemiology. The inference target is a causal estimand which measures the change in the expected outcome of unit under study of different interventions. It has a well-established basis in frequentist semi-parametric theory, with estimation of causal parameters typically conducted via outcome regression and propensity score adjustment. A Bayesian counterpart, however, is not obvious as doubly robust estimation involves a semi-parametric formulation in the absence of a fully specified likelihood function. In this project, we aim to investigate solutions for Bayesian causal inference from standard prior-to-posterior updating, without requiring a parametric family for the observations, and also robust to model misspecfication. We will apply the propose methods to evaluate and quantify London's Stop & Search causal effects on deterring drug offenses in previous decade.