因果推断

Causal inference is the process of drawing a conclusion about a causal connection based on the conditions of the occurrence of an effect. The main difference between causal inference and inference of association is that the former analyzes the response of the effect variable when the cause is changed. The science of why things occur is called etiology. Causal inference is an example of causal reasoning.

因果推断Causal inference是根据某一效应发生的条件得出关于因果关系的结论的过程。因果推断与关联推理inference of association的主要区别在于前者分析在原因变化时结果变量的反应。研究事情为什么发生的科学叫做病因学etiology。因果推断是因果推理causal reasoning的一个例子。

Definition定义

Inferring the cause of something has been described as:

对某事原因的推断过程已经被描述为是:Inferring the cause of something has been described as:

 --嘉树（讨论） inferring是ing形式，因此译为“推断的过程”，存疑

• "...reason[ing] to the conclusion that something is, or is likely to be, the cause of something else".

• “推理得出某事是（或可能是）其他事情的原因这一结论的过程。”

• "Identification of the cause or causes of a phenomenon, by establishing covariation of cause and effect, a time-order relationship with the cause preceding the effect, and the elimination of plausible alternative causes."

• “通过建立因果的共变关系、建立原因先于结果的时间顺序关系，以及消除其他可能的替代原因的过程，从而对现象的一个或多个原因进行确定的过程。”

Methods 方法

Epidemiological studies employ different epidemiological methods of collecting and measuring evidence of risk factors and effect and different ways of measuring association between the two. A hypothesis is formulated, and then tested with statistical methods. It is statistical inference that helps decide if data are due to chance, also called random variation, or indeed correlated and if so how strongly. However, correlation does not imply causation, so further methods must be used to infer causation.

流行病学epidemiological收集和衡量危险因素和结果，以及衡量危险因素和结果之间关系的方法与其他学科不同。一个假设提出来以后用统计学假设检验Statistical hypothesis testing。这种统计学推断statistical inference 有助于判断数据是由偶然性引起的，也就是随机变异random variation，还是确实存在相关性，以及相关性有多强。然而，相关不意味着因果，因此必须进一步使用其他方法来推断因果关系。

Common frameworks for causal inference are structural equation modeling and the Rubin causal model.

因果推断的常见框架有结构方程模型structural equation modeling和Rubin因果模型 Rubin causal model。

In epidemiology 在流行病学中

Epidemiology studies patterns of health and disease in defined populations of living beings in order to infer causes and effects. An association between an exposure to a putative risk factor and a disease may be suggestive of, but is not equivalent to causality because correlation does not imply causation. Historically, Koch's postulates have been used since the 19th century to decide if a microorganism was the cause of a disease. In the 20th century the Bradford Hill criteria, described in 1965 have been used to assess causality of variables outside microbiology, although even these criteria are not exclusive ways to determine causality.

流行病学Epidemiology研究特定生物群体的健康和疾病模式patterns，以推断原因和结果。暴露exposure 于一般认为的危险因素risk factor和疾病之间的联系可能被提出，但不等同于确认因果关系，因为相关不意味着因果。从历史上看，科赫法则 Koch's postulates从19世纪开始就被用来判断一种微生物是否是一种疾病的原因。在20世纪，布拉德福德·希尔准则Bradford Hill criteria（参见Bradford Hill 1965年的文章中）已经被用来评估微生物学之外的变量的因果关系，尽管即使是这些标准也不是确定因果关系的唯一方法。

In molecular epidemiology the phenomena studied are on a molecular biology level, including genetics, where biomarkers are evidence of cause or effects.

分子流行病学molecular epidemiology中研究的现象是在分子生物学水平上的，也涵盖了遗传学。而遗传学中的生物标志物biomarkers就是原因或结果的证据。

A recent trend模板:When is to identify evidence for influence of the exposure on molecular pathology within diseased tissue or cells, in the emerging interdisciplinary field of molecular pathological epidemiology (MPE).模板:Third-party-inline Linking the exposure to molecular pathologic signatures of the disease can help to assess causality. 模板:Third-party-inline Considering the inherent nature of heterogeneity of a given disease, the unique disease principle, disease phenotyping and subtyping are trends in biomedical and public health sciences, exemplified as personalized medicine and precision medicine.模板:Third-party-inline

在新兴的分子病理流行病学molecular pathological epidemiology (MPE)交叉学科领域，最近的一个趋势（截至2014年）是确定在病变组织或细胞内，暴露exposure 在分子病理学molecular pathology上的影响。将暴露与疾病的分子病理特征联系起来可以帮助因果关系的评估。鉴于给定疾病的异质性的固有特征、独特的疾病原理等，疾病表现型phenotyping和亚型subtyping 现在是生物医学和公共卫生科学public health的趋势，例证包括个体化医学personalized medicine和精准医学precision medicine等。

In computer science在计算机科学领域

Determination of cause and effect from joint observational data for two time-independent variables, say X and Y, has been tackled using asymmetry between evidence for some model in the directions, X → Y and Y → X. The primary approaches are based on Algorithmic information theory models and noise models.

确定两个时间独立变量：X 和 Y 的联合观测数据因果关系的问题已经被解决了，方法是利用 X → Y 和 Y → X 方向上某些模型的证据不对称性。主要的方法基于算法信息理论Algorithmic information theory模型和噪声模型noise models。

Algorithmic information models算法信息模型

Compare two programs, both of which output both X and Y.

比较两个同时输出 X 和 Y 的程序。

• Store Y and a compressed form of X in terms of uncompressed Y.

• Store X and a compressed form of Y in terms of uncompressed X.

• 用未压缩的 X 来存储 X 和压缩形式的 Y 。

The shortest such program implies the uncompressed stored variable more-likely causes the computed variable.

最短的这种程序意味着，更有可能是未压缩的存储变量stored variable导致了计算出的变量computed variable。

Noise models噪音模型

Incorporate an independent noise term in the model to compare the evidences of the two directions.

在模型中引入一个独立的噪声项，以比较两个方向的证据。

Here are some of the noise models for the hypothesis Y → X with the noise E:

下面是一些支持 Y → X 假设且具有噪声 E 的噪声模型:

• Additive noise: [math]\displaystyle{ Y = F(X)+E }[/math]
• 加法噪音Additive noise

• Linear noise: [math]\displaystyle{ Y = pX + qE }[/math]
• 线性噪音Linear noise

• Post-non-linear: [math]\displaystyle{ Y = G(F(X)+E) }[/math]
• 后非线性Post-non-linear（噪音）

• Heteroskedastic noise: [math]\displaystyle{ Y = F(X)+E.G(X) }[/math]
• 异方差噪音Heteroskedastic noise

• Functional noise: [math]\displaystyle{ Y = F(X,E) }[/math]
• 功能性噪音Functional noise

The common assumption in these models are:

这些模型的共同假设是:

• There are no other causes of Y.
• Y 没有其他原因。

• X and E have no common causes.
• X 和 E 没有共同的原因。

• Distribution of cause is independent from causal mechanisms.
• 原因的分布独立于因果机制。

On an intuitive level, the idea is that the factorization of the joint distribution P(Cause, Effect) into P(Cause)*P(Effect | Cause) typically yields models of lower total complexity than the factorization into P(Effect)*P(Cause | Effect). Although the notion of “complexity” is intuitively appealing, it is not obvious how it should be precisely defined. A different family of methods attempt to discover causal "footprints" from large amounts of labeled data, and allow the prediction of more flexible causal relations.

在直观的层面上，这个想法是联合分布P(Cause, Effect) 到 P(Cause)*P(Effect | Cause)的因式分解通常产生的模型的总复杂性complexity 低于到P(Effect)*P(Cause | Effect)的因式分解。尽管“复杂性”的概念在直觉上很吸引人，但是对于如何定义它却并不显而易见。另一种不同类族的方法尝试从大量标签过的数据中发现因果的“足迹”，并且允许预测更灵活的因果关系。

In statistics and economics

在统计学和经济学领域

Main article: Causality § Statistics and economics

In statistics and economics, causality is often tested via regression analysis. Several methods can be used to distinguish actual causality from spurious correlations. First, economists constructing regression models establish the direction of causal relation based on economic theory (theory-driven econometrics). For example, if one studies the dependency between rainfall and the future price of a commodity, then theory (broadly construed) indicates that rainfall can influence prices, but futures prices cannot make changes to the amount of rain . Second, the instrumental variables (IV) technique may be employed to remove any reverse causation by introducing a role for other variables (instruments) that are known to be unaffected by the dependent variable. Third, economists consider time precedence to choose appropriate model specification. Given that partial correlations are symmetrical, one cannot determine the direction of causal relation based on correlations only. Based on the notion of probabilistic view on causality, economists assume that causes must be prior in time than their effects. This leads to using the variables representing phenomena happening earlier as independent variables and developing econometric tests for causality (e.g., Granger-causality tests) applicable in time series analysis. Fifth, other regressors are included to ensure that confounding variables are not causing a regressor to appear to be significant spuriously but, in the areas suffering from the problem of multicollinearity such as macroeconomics, it is in principle impossible to include all confounding factors and therefore econometric models are susceptible to the common-cause fallacy.. Recently, the movement of design-based econometrics has popularized using natural experiments and quasi-experimental research designs to address the problem of spurious correlations.

在统计学和经济学中，因果关系通常通过回归分析来检验。有几种方法可以用来区分真实的因果关系和虚假的相关性。第一，经济学家根据经济理论(理论驱动theory-driven的计量经济学)构建回归模型，从而确定因果关系的方向。 例如，如果研究降雨量与商品未来价格之间的依赖关系，那么理论(广义解释)表明，降雨量可以影响价格，但期货价格不能改变降雨量。其次，工具变量(IV)技术可以用来消除任何反向因果关系，通过引入其他变量(工具)的作用，已知是不受因变量的影响。第三，经济学家考虑时间优先选择合适的模型规范。由于部分相关是对称的，人们不能确定方向的因果关系的基础上，只有相关性。基于对因果关系的概率观点，经济学家假设原因必须在时间上优先于它们的结果。这导致使用表示早期发生的现象的变量作为自变量，并开发适用于时间序列分析的因果关系检验(例如，格兰杰因果检验)的计量经济学检验。第五，包括其他回归因素是为了确保混淆变量不会导致回归因素出现明显的虚假性，但在遭受多重共线性问题困扰的领域，如宏观经济学，原则上不可能包括所有混杂因素，因此计量经济模型容易出现共因谬误。 .近年来，以设计为基础的计量经济学运动已经推广使用自然实验和准实验研究设计来解决虚假关联的问题。

In social science

在社会科学领域 The social sciences have moved increasingly toward a quantitative framework for assessing causality. Much of this has been described as a means of providing greater rigor to social science methodology. Political science was significantly influenced by the publication of Designing Social Inquiry, by Gary King, Robert Keohane, and Sidney Verba, in 1994. King, Keohane, and Verba (often abbreviated as KKV) recommended that researchers applying both quantitative and qualitative methods adopt the language of statistical inference to be clearer about their subjects of interest and units of analysis. Proponents of quantitative methods have also increasingly adopted the potential outcomes framework, developed by Donald Rubin, as a standard for inferring causality.

社会科学越来越倾向于一个评估因果关系的定量框架。其中很大一部分被描述为一种提供更严密的社会科学方法论的手段。1994年，加里 · 金、罗伯特 · 基奥汉和西德尼 · 维尔巴合著的《设计社会探究》对政治科学产生了重大影响。King，Keohane，和 Verba (通常缩写为 KKV)建议研究人员应用定量和定性的方法采用推论统计学的语言来更清楚地说明他们感兴趣的主题和分析的单位。定量方法的支持者也越来越多地采用唐纳德 · 鲁宾开发的潜在结果框架作为推断因果关系的标准。

Debates over the appropriate application of quantitative methods to infer causality resulted in increased attention to the reproducibility of studies. Critics of widely-practiced methodologies argued that researchers have engaged in P hacking to publish articles on the basis of spurious correlations. To prevent this, some have advocated that researchers preregister their research designs prior to conducting to their studies so that they do not inadvertently overemphasize a non-reproducible finding that was not the initial subject of inquiry but was found to be statistically significant during data analysis. Internal debates about methodology and reproducibility within the social sciences have at times been acrimonious.

关于适当应用定量方法来推断因果关系的争论导致了对研究重复性的更多关注。对广泛使用的方法论持批评态度的人认为，研究人员利用 p-hacking技术，在虚假关联的基础上发表文章。为了防止这种情况，一些人主张研究人员在进行研究之前预先注册他们的研究设计，这样他们就不会无意中过分强调一项不可复制的发现，这项发现并非最初的调查对象，但在数据分析中被发现具有统计意义。社会科学内部关于方法论和可重现性的争论有时是尖刻的。

While much of the emphasis remains on statistical inference in the potential outcomes framework, social science methodologists have developed new tools to conduct causal inference with both qualitative and quantitative methods, sometimes called a “mixed methods” approach. Advocates of diverse methodological approaches argue that different methodologies are better suited to different subjects of study. Sociologist Herbert Smith and Political Scientists James Mahoney and Gary Goertz have cited the observation of Paul Holland, a statistician and author of the 1986 article “Statistics and Causal Inference,” that statistical inference is most appropriate for assessing the “effects of causes” rather than the “causes of effects.” Qualitative methodologists have argued that formalized models of causation, including process tracing and fuzzy set theory, provide opportunities to infer causation through the identification of critical factors within case studies or through a process of comparison among several case studies. These methodologies are also valuable for subjects in which a limited number of potential observations or the presence of confounding variables would limit the applicability of statistical inference.

虽然在潜在结果框架中，大部分重点仍然放在推论统计学上，但社会科学方法论者已经开发出新的工具，用定性和定量的方法进行因果推断，有时被称为混合方法。不同方法论的支持者认为不同的方法论更适合不同的研究对象。社会学家 Herbert Smith 和政治学家 James Mahoney 和 Gary Goertz 引用了统计学家 Paul Holland 的观察结果，他在1986年发表了一篇名为《统计学和因果推断》的文章，认为推论统计学最适合于评估“原因的影响”而不是“影响的原因” 定性方法学家认为，形式化的因果关系模型，包括过程追踪和模糊集合理论，提供了推断因果关系的机会，通过在案例研究中识别关键因素或通过几个案例研究之间的比较过程。这些方法对于那些数量有限的潜在观察或混杂变量的存在会限制推论统计学的适用性的课题也是有价值的。

See also

参见

• Causal analysis 因果分析

• Granger causality 格兰杰因果分析

• Multivariate statistics 多元统计

• Partial least squares regression 偏最小二乘回归

• Pathogenesis 发病学

• Pathology 病理学

• Regression analysis 回归分析

• Transfer entropy 传递熵

References

参考资料

Bibliography

参考书目

• Hernán, MA; Robins, JM (2020-01-21). Causal Inference: What If. Barnsley: Boca Raton: Chapman & Hall/CRC. https://www.hsph.harvard.edu/miguel-hernan/causal-inference-book/. 

External links

外部链接 模板:Commons category

• NIPS 2013 Workshop on Causality

• Causal inference at the Max-Planck-Institute for Intelligent Systems Tübingen

编者推荐

集智课程推荐

社交网络中的因果推断 本课程中，将简要介绍一些基本的因果推断策略，并聚焦社会网络分析中的因果推断问题，涉及社会网络实验设计、固定样本、工具变量和敏感度分析等。

书籍推荐

为什么:关于因果关系的新科学 在本书中，人工智能领域的权威专家Judea Pearl及其同事领导的因果关系革命突破多年的迷雾，厘清了知识的本质，确立了因果关系研究在科学探索中的核心地位。

类别: 图形模型

类别: 回归分析

类别: 归纳推理

分类: 统计哲学

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