因果推断三种分析框架及其应用综述

介绍因果推断所涉及的基本概念及其三种分析框架:反事实框架、潜在结果模型和结构因果模型。首先，从反事实框架介绍因果效应的发端；然后，从基于反事实的两个因果推断分析框架:潜在结果模型和结构因果模型，来分别阐述两个分析框架所涉及的关键理论和应用方法。其中，潜在结果模型使用数学和可计算的语言对因果理论进行阐述，是一种将假设、命题和结论清晰化表达的计算模型，其在原因和结果变量已知的前提下定量分析原因变量对结果变量的因果效应，并对缺失的潜在结果进行补齐，使观察性研究的效果接近试验性研究。结构因果模型则是一种基于图论的因果推断方法，它将事件分为观察、干预和反事实三个层级，并通过do运算将干预和反事实层级的因果关系都降维成可以通过统计学手段解决的问题。最后，探讨了现今多领域内因果推断的应用场景，并总结了三种分析框架的异同点。 

Three analytical frameworks of causal inference and their applications

Causality is a generic relationship between an effect and a cause that produces it. The causal relationship among things has been a research hotspot; however, the complexity of causality is sometimes far beyond our imagination. Although some causality problems seem easy to analyze, finding an exact answer may not be easy. Nevertheless, through the continuous innovation and development of empirical research methods in recent decades, we have had several clear analytical frameworks and effective methods on how to define and estimate causality. Exploring the causal effects among things is a promising research topic in many fields, such as statistics, computer science, and econometrics. With Joshua D. Angrist and Guido W. Imbens winning the Nobel Prize in economics for their methodological contributions to the analysis of causality in 2021, causal inference is expected to thrive in these fields. This paper briefly introduces the basic concepts involved in causal inference and its three analytical frameworks, namely, counterfactual framework (CF), potential outcome framework (POF), and structural causal model (SCM). Firstly, we introduce the origin of causal effects according to CF. Secondly, based on the counterfactual theory, two analysis frameworks are considered (POF and SCM), and we introduce the associated key theories and methods. The SCM explains the causal theory through mathematics and computable language, and it is a calculation model that clearly expresses hypotheses, propositions, and conclusions. It quantitatively analyzes the pair of cause variables under the premise that the cause and effect variables are known. The POF makes up for the missing potential results, such that the effect of the observational research is close to experimental research. The SCM is a causal inference method based on graph theory. It divides events into three levels: observation, intervention, and counterfactual. Through the “do” operation, the causal relationship at the intervention and counterfactual levels could be reduced to low-dimensional problems, which can be solved via statistical methods. Finally, the current application scenarios of causal inference in many fields are discussed in this paper, and the three analysis frameworks are compared.