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第1行： − 此词条暂由彩云小译翻译，翻译字数共843，未经人工整理和审校，带来阅读不便，请见谅。+ − − − − − − − In [[philosophy of science]], a '''causal model''' (or '''structural causal model''') is a [[conceptual model]] that describes the [[causality|causal]] mechanisms of a [[system]]. Causal models can improve study designs by providing clear rules for deciding which independent variables need to be included/controlled for. − − In philosophy of science, a causal model (or structural causal model) is a conceptual model that describes the causal mechanisms of a system. Causal models can improve study designs by providing clear rules for deciding which independent variables need to be included/controlled for. − − They can allow some questions to be answered from existing observational data without the need for an interventional study such as a [[randomized controlled trial]]. Some interventional studies are inappropriate for ethical or practical reasons, meaning that without a causal model, some hypotheses cannot be tested. − − They can allow some questions to be answered from existing observational data without the need for an interventional study such as a randomized controlled trial. Some interventional studies are inappropriate for ethical or practical reasons, meaning that without a causal model, some hypotheses cannot be tested. − − Causal models can help with the question of ''external validity'' (whether results from one study apply to unstudied populations). Causal models can allow data from multiple studies to be merged (in certain circumstances) to answer questions that cannot be answered by any individual data set. − − Causal models can help with the question of external validity (whether results from one study apply to unstudied populations). Causal models can allow data from multiple studies to be merged (in certain circumstances) to answer questions that cannot be answered by any individual data set. − − Causal models are ''falsifiable'', in that if they do not match data, they must be rejected as invalid. They must also be credible to those close to the phenomena the model intends to explain.<ref>{{Cite journal|last1=Barlas|first1=Yaman|last2=Carpenter|first2=Stanley|date=1990|title=Philosophical roots of model validation: Two paradigms|journal=System Dynamics Review|language=en|volume=6|issue=2|pages=148–166|doi=10.1002/sdr.4260060203}}</ref> − − Causal models are falsifiable, in that if they do not match data, they must be rejected as invalid. They must also be credible to those close to the phenomena the model intends to explain. − − Causal models have found applications in [[signal processing]], [[epidemiology]] and [[machine learning]].<ref name=":0">{{harvnb|Pearl|2009}}</ref> − − Causal models have found applications in signal processing, epidemiology and machine learning. − + − − − − [[Judea Pearl]] defines a causal model as an ordered triple <math>\langle U, V, E\rangle</math>, where U is a set of [[exogenous variable]]s whose values are determined by factors outside the model; V is a set of endogenous variables whose values are determined by factors within the model; and E is a set of [[structural equation]]s that express the value of each endogenous variable as a function of the values of the other variables in U and V.<ref name=":0" /> − − Judea Pearl defines a causal model as an ordered triple <math>\langle U, V, E\rangle</math>, where U is a set of exogenous variables whose values are determined by factors outside the model; V is a set of endogenous variables whose values are determined by factors within the model; and E is a set of structural equations that express the value of each endogenous variable as a function of the values of the other variables in U and V. − + − − 作为一个实证主义者，皮尔逊将因果的概念从许多科学中去除，他认为因果关系是一种无法证明的特殊的关联，并引入相关系数作为关联强度的度量方法。他写道: “作为运动原因的力，与作为成长原因的树神完全一样”，而因果关系只是“现代科学高深奥秘中的迷信”。皮尔森在伦敦大学学院创建了期刊“Biometrika”和生物统计学实验室，后者成为了统计学的世界领军者。[5] − − 1908年，哈代和温伯格通过复活孟德尔的继承权，解决了导致高尔顿放弃因果关系的特质稳定问题。[5] − − 在1921年，赖特的路径分析成为因果模型和因果图的理论祖先。[6]他开发了这种方法，同时试图阐明遗传，发育和环境对豚鼠皮毛模式的相对影响。他通过证明这样的分析如何解释豚鼠出生体重，子宫内时间和产仔数之间的关系来支持他当时的观点。杰出的统计学家对这些想法的反对使他们在接下来的40年中被忽略（在动物饲养员中除外）。取而代之的是，科学家依赖于相关性，部分是受赖特（Wright）评论家（和主要统计学家）费舍尔（Fisher）的要求。[5]唯一的例外是伯克斯（Burks），他是一名学生，他于1926年首先应用路径图来表示中介影响（mediator），并断言保持常量不变会导致错误。她可能独立地发明了路线图。[5]：304 − − 1923年，内曼（Neyman）提出了潜在结果的概念，但是直到1990年他的论文才从波兰语翻译成英语。[5]：271 − − 1958年，考克斯（Cox）警告说，控制变量Z仅在极不可能受到自变量影响的情况下才有效。[5]：154 − − 在1960年代，Duncan，Blalock，Goldberger等人重新发现了路径分析。邓肯在阅读布拉洛克关于路径图的著作时，想起了二十年前奥格本的一次演讲，其中提到了赖特的论文，而后者又提到了伯克斯。[5]：308 − − 社会学家最初将因果模型称为结构方程模型，但一旦成为死记硬背的方法，它就失去了效用，导致一些从业者拒绝与因果关系的任何联系。经济学家采用了路径分析的代数部分，称其为联立方程模型。但是，经济学家仍然避免将因果意义归因于他们的方程式。[5] − − 赖特在发表第一篇论文60年后，根据卡林（Karlin）等人的批评，发表了一篇概述该论文的文章，该论据反对仅处理线性关系，而健壮的，无模型的数据表示方式则更具启发性。[5] − − 1973年，刘易斯（Lewis）提倡用因果关系（反事实）代替相关性。他提到了人类预见替代世界的能力，在这个世界中，有因没有发生，而其影响只有在其原因之后才出现。[5]：266鲁宾在1974年提出了“潜在结果”的概念，作为问因果问题的语言。[5]：269 − − 1983年，卡特赖特（Cartwright）提出，以任何与效果“因果相关”的因素为条件，超越简单概率作为唯一指导。[5]：48 − − 1986年，Baron和Kenny引入了检测和评估线性方程组中的中介的原理。截至2014年，他们的论文在所有时间中被引用次数排在第33位。[5]：324那年，格陵兰和罗宾斯提出了“可交换性”方法，通过考虑反事实来处理混杂问题。他们建议评估如果他们没有接受治疗会给治疗组带来什么后果，并将其结果与对照组进行比较。如果他们匹配，据说没有混淆。[5]：154 − − 哥伦比亚大学设有因果人工智能实验室，该实验室正试图将因果建模理论与人工神经网络联系起来。[7] − − − [[Aristotle]] defined a taxonomy of causality, including material, formal, efficient and final causes. Hume rejected Aristotle's taxonomy in favor of [[Counterfactual conditional|counterfactuals]]. At one point, he denied that objects have "powers" that make one a cause and another an effect.<ref name=":1" />Later he adopted "if the first object had not been, the second had never existed" ("[[Sine qua non|but-for]]" causation).<ref name=":1" /> − − 亚里斯多德定义了因果关系的分类法，包括质料因、形式因、动力因、目的因。休谟更偏爱反事实，他拒绝了亚里士多德的分类法。有段时间，他甚至否认物体本身具有使得一个物体成为原因而另一个物体成为结果的“力量”。后来，他接收了“第一物体还没存在时，第二个根本不存在”（“but-for”因果关系）。 − − In the late 19th century, the discipline of statistics began to form. After a years-long effort to identify causal rules for domains such as biological inheritance, [[Francis Galton|Galton]] introduced the concept of [[Regression toward the mean|mean regression]] (epitomized by the [[sophomore slump]] in sports) which later led him to the non-causal concept of [[correlation]].<ref name=":1">{{Cite book|url={{google books |plainurl=y |id=9H0dDQAAQBAJ}} |title=The Book of Why: The New Science of Cause and Effect|last1=Pearl|first1=Judea|last2=Mackenzie|first2=Dana|date=2018-05-15|publisher=Basic Books|isbn=9780465097616|language=en|author-link=Judea Pearl}}</ref> − − 在19世纪末，统计学学科开始形成。经过多年努力确定诸如生物遗传等领域的因果规则后，高尔顿引入了均值回归的概念（体育运动中二年级低迷使之退步），后来将他引向了非因果的相关性概念。[5] − − − − − As a [[Positivism|positivist]], [[Karl Pearson|Pearson]] expunged the notion of causality from much of science as an unprovable special case of association and introduced the [[correlation coefficient]] as the metric of association. He wrote, "Force as a cause of motion is exactly the same as a tree god as a cause of growth" and that causation was only a "fetish among the inscrutable arcana of modern science". Pearson founded ''[[Biometrika]]'' and the Biometrics Lab at [[University College London]], which became the world leader in statistics.<ref name=":1" /> − − − − In 1908 [[G. H. Hardy|Hardy]] and [[Wilhelm Weinberg|Weinberg]] solved the problem of [[Hardy–Weinberg principle|trait stability]] that had led Galton to abandon causality, by resurrecting [[Mendelian inheritance]].<ref name=":1" /> − − The highest level, counterfactual, involves consideration of an alternate version of a past event, or what would happen under different circumstances for the same experimental unit. For example, what is the probability that, if a store had doubled the price of floss, the toothpaste-purchasing shopper would still have bought it? − − 最高层次的反事实，包括考虑过去事件的另一个版本，或者同一个实验单位在不同情况下会发生什么。例如，如果一家商店将牙线的价格提高了一倍，购买牙膏的购物者仍然会购买牙线的概率是多少？ − − − − In 1921 [[Sewall Wright|Wright]]'s [[Path analysis (statistics)|path analysis]] became the theoretical ancestor of causal modeling and causal graphs.<ref>{{Cite book|url={{google books |plainurl=y |id=yWWEIvNgUQ4C|page=707}} |title=The Oxford Handbook of Causation |volume=1 |editor-last=Beebee |editor-first=Helen|editor-last2=Hitchcock|editor-first2=Christopher|editor-last3=Menzies|editor-first3=Peter|date=2012-01-12|publisher=OUP Oxford|isbn=9780191629464|language=en|first=Samir |last=Okasha |chapter=Causation in Biology|chapter-url=http://www.oxfordhandbooks.com/view/10.1093/oxfordhb/9780199279739.001.0001/oxfordhb-9780199279739-e-0036|doi=10.1093/oxfordhb/9780199279739.001.0001 }}</ref> He developed this approach while attempting to untangle the relative impacts of [[heredity]], development and environment on [[guinea pig]] coat patterns. He backed up his then-heretical claims by showing how such analyses could explain the relationship between guinea pig birth weight, ''[[Uterus|in utero]]'' time and litter size. Opposition to these ideas by prominent statisticians led them to be ignored for the following 40 years (except among animal breeders). Instead scientists relied on correlations, partly at the behest of Wright's critic (and leading statistician), [[Ronald Fisher|Fisher]].<ref name=":1" /> One exception was Burks, a student who in 1926 was the first to apply path diagrams to represent a mediating influence (''mediator'') and to assert that holding a mediator constant induces errors. She may have invented path diagrams independently.<ref name=":1" /> − − :<math>P (floss |toothpaste, price*2)</math> − − − − − In 1923, [[Jerzy Neyman|Neyman]] introduced the concept of a potential outcome, but his paper was not translated from Polish to English until 1990.<ref name=":1" /> − − Counterfactuals can indicate the existence of a causal relationship. Models that can answer counterfactuals allow precise interventions whose consequences can be predicted. At the extreme, such models are accepted as physical laws (as in the laws of physics, e.g., inertia, which says that if force is not applied to a stationary object, it will not move). − − 反事实可以表明因果关系的存在。能够回答反事实的模型允许精确的干预，其结果可以预测。在极端情况下，这些模型被认为是物理定律(就像物理定律一样，例如惯性，它说如果力不作用于静止的物体，它就不会移动)。 − − − − In 1958 [[David Cox (statistician)|Cox]] warned that controlling for a variable Z is valid only if it is highly unlikely to be affected by independent variables.<ref name=":1" /> − − − − In the 1960s, [[Otis Dudley Duncan|Duncan]], [[Hubert M. Blalock Jr.|Blalock]], [[Arthur Goldberger|Goldberger]] and others rediscovered path analysis. While reading Blalock's work on path diagrams, Duncan remembered a lecture by [[William Fielding Ogburn|Ogburn]] twenty years earlier that mentioned a paper by Wright that in turn mentioned Burks.<ref name=":1" /> − − For x to be a necessary cause of y, the presence of y must imply the prior occurrence of x. The presence of x, however, does not imply that y will occur. Necessary causes are also known as "but-for" causes, as in y would not have occurred but for the occurrence of x. − − 如果 x 是 y 的必然原因，那么 y 的存在必然意味着 x 的事先出现。然而，x 的存在并不意味着 y 会出现。必要的原因也被称为“ but-for”原因，因为在 y 中，如果没有发生 x，就不会发生 y。 + + − Sociologists originally called causal models [[structural equation modeling]], but once it became a rote method, it lost its utility, leading some practitioners to reject any relationship to causality. Economists adopted the algebraic part of path analysis, calling it simultaneous equation modeling. However, economists still avoided attributing causal meaning to their equations.<ref name=":1" />+ + + − Sixty years after his first paper, Wright published a piece that recapitulated it, following [[Samuel Karlin|Karlin]] et al.'s critique, which objected that it handled only linear relationships and that robust, model-free presentations of data were more revealing.<ref name=":1" />+ + + − A causal diagram is a directed graph that displays causal relationships between variables in a causal model. A causal diagram includes a set of variables (or nodes). Each node is connected by an arrow to one or more other nodes upon which it has a causal influence. An arrowhead delineates the direction of causality, e.g., an arrow connecting variables A and B with the arrowhead at B indicates that a change in A causes a change in B (with an associated probability). A path is a traversal of the graph between two nodes following causal arrows.+ − 因果图是一个有向图，它显示了因果模型中变量之间的因果关系。因果关系图包括一组变量(或节点)。每个节点通过一个箭头连接到一个或多个其他节点，对这些节点有因果影响。箭头描述了因果关系的方向，例如，一个箭头连接变量 a 和 b 与箭头在 b 表示 a 的变化导致 b 的变化(与一个相关的概率)。路径是在两个节点之间按照因果箭头进行的图的遍历。+ − In 1973 [[David Lewis (philosopher)|Lewis]] advocated replacing correlation with but-for causality (counterfactuals). He referred to humans' ability to envision alternative worlds in which a cause did or not occur and in which effect an appeared only following its cause.<ref name=":1" /> In 1974 [[Donald Rubin|Rubin]] introduced the notion of "potential outcomes" as a language for asking causal questions.<ref name=":1" />+ + + − Because genes vary randomly across populations, presence of a gene typically qualifies as an instrumental variable, implying that in many cases, causality can be quantified using regression on an observational study.+ − 因为基因在不同人群中随机变化，基因的存在通常被认为是工具变量，这意味着在许多情况下，因果关系可以用观察性研究回归来量化。+ − In 1983 [[Nancy Cartwright (philosopher)|Cartwright]] proposed that any factor that is "causally relevant" to an effect be conditioned on, moving beyond simple probability as the only guide.<ref name=":1" />+ + − + + + + − In 1986 Baron and Kenny introduced principles for detecting and evaluating mediation in a system of linear equations. As of 2014 their paper was the 33rd most-cited of all time.<ref name=":1" />That year [[Sander Greenland|Greenland]] and [[James Robins|Robins]] introduced the "exchangeability" approach to handling confounding by considering a counterfactual. They proposed assessing what would have happened to the treatment group if they had not received the treatment and comparing that outcome to that of the control group. If they matched, confounding was said to be absent.<ref name=":1" />+ + + + + − The following converts a do expression into a do-free expression by conditioning on the variables along the front-door path.+ − 下面通过对前门路径上的变量进行条件处理，将 do 表达式转换为 do-free 表达式。+ − Columbia University operates the Causal Artificial Intelligence Lab which is attempting to connect causal modeling theory to [[artificial neural network]]s.<ref>{{Cite web|url=https://www.technologyreview.com/s/615189/what-ai-still-cant-do/|title=What AI still can't do|last=Bergstein|first=Brian|website=MIT Technology Review|language=en-US|access-date=2020-02-20}}</ref>+ − + + + + + − Pearl's causal [[Metamodeling|metamodel]] involves a three-level abstraction he calls the ladder of causation. The lowest level, Association (seeing/observing), entails the sensing of regularities or patterns in the input data, expressed as correlations. The middle level, Intervention (doing), predicts the effects of deliberate actions, expressed as causal relationships. The highest level, [[Counterfactual conditional|Counterfactuals]] (imagining), involves constructing a theory of (part of) the world that explains why specific actions have specific effects and what happens in the absence of such actions.<ref name=":1" />+ + + − === Association ===+ + + − One object is associated with another if observing one changes the [[probability]] of observing the other. Example: shoppers who buy toothpaste are more likely to also buy dental floss. Mathematically:+ + + + + + − :<math>P (floss | toothpaste) </math>+ + + − or the probability of (purchasing) floss given (the purchase of) toothpaste. Associations can also be measured via computing the [[Correlation and dependence|correlation]] of the two events. Associations have no causal implications. One event could cause the other, the reverse could be true, or both events could be caused by some third event (unhappy hygenist shames shopper into treating their mouth better ).<ref name=":1" />+ + + + − + + + + + + + + + + + + + + + + + + − This level asserts specific causal relationships between events. Causality is assessed by experimentally performing some action that affects one of the events. Example: if we doubled the price of toothpaste, what would be the new probability of purchasing? Causality cannot be established by examining history (of price changes) because the price change may have been for some other reason that could itself affect the second event (a tariff that increases the price of both goods). Mathematically:+ + + + + + + + + + − :<math>P (floss | do(toothpaste)) </math>+ + + − + − where ''do'' is an operator that signals the experimental intervention (doubling the price).<ref name=":1" /> The operator indicates performing the minimal change in the world necessary to create the intended effect, a "mini-surgery" on the model with as little change from reality as possible.<ref>{{cite journal |last1=Pearl |first1=Judea |title=Causal and Counterfactual Inference |date=29 Oct 2019 |url=https://ftp.cs.ucla.edu/pub/stat_ser/r485.pdf |access-date=14 December 2020}}</ref> − − − − === Counterfactuals === − − − − * − − * − − The highest level, counterfactual, involves consideration of an alternate version of a past event, or what would happen under different circumstances for the same experimental unit. For example, what is the probability that, if a store had doubled the price of floss, the toothpaste-purchasing shopper would still have bought it? − − − − :<math>P (floss | toothpaste, price*2) </math> 第230行：
第171行： − Counterfactuals can indicate the existence of a causal relationship. Models that can answer counterfactuals allow precise interventions whose consequences can be predicted. At the extreme, such models are accepted as physical laws (as in the laws of physics, e.g., inertia, which says that if force is not applied to a stationary object, it will not move).<ref name=":1" /> −
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{{Cleanup rewrite|date=March 2020}}
{{Cleanup rewrite|date=March 2020}}
[[File:Diagram of Dynamic Causal Modelling - Causal Modelling and Brain Connectivity in Functional Magnetic Resonance Imaging by Karl Friston.png|thumb|300px|比较两个竞争的因果模型(DCM，GCM)用于解释[[fMRI 图像]]<ref>{{cite journal | doi=10.1371/journal.pbio.1000033 | pmid=19226186 | pmc=2642881 | author=Karl Friston | title=Causal Modelling and Brain Connectivity in Functional Magnetic Resonance Imaging | journal=PLOS Biology| volume=7 | number=2 | pages=e1000033 | date=Feb 2009}}</ref>]]
[[File:Diagram of Dynamic Causal Modelling - Causal Modelling and Brain Connectivity in Functional Magnetic Resonance Imaging by Karl Friston.png|thumb|300px|比较两个竞争的因果模型(DCM，GCM)用于解释[[fMRI 图像]]<ref>{{cite journal | doi=10.1371/journal.pbio.1000033 | pmid=19226186 | pmc=2642881 | author=Karl Friston | title=Causal Modelling and Brain Connectivity in Functional Magnetic Resonance Imaging | journal=PLOS Biology| volume=7 | number=2 | pages=e1000033 | date=Feb 2009}}</ref>]]
在科学哲学中，因果模型(或结构因果模型)是描述系统因果机制的概念模型。因果模型可以通过提供清晰的规则来决定需要考虑/控制哪些自变量，从而改进研究设计。
在科学哲学中，因果模型(或结构因果模型)是描述系统因果机制的概念模型。因果模型可以通过提供清晰的规则来决定需要考虑/控制哪些自变量，从而改进研究设计。
它们可以从现有的观察数据中回答一些问题，而无需进行随机对照试验似的干预性研究。一些干预性研究由于伦理或实践的原因是不合适的，这意味着如果没有一个因果模型，一些假设无法被检验。
它们可以从现有的观察数据中回答一些问题，而无需进行随机对照试验似的干预性研究。一些干预性研究由于伦理或实践的原因是不合适的，这意味着如果没有一个因果模型，一些假设无法被检验。
因果模型可以帮助解决外部有效性问题(一项研究的结果是否适用于未研究的总体)。因果模型可以允许多个研究的数据(在某些情况下)合并来回答任何单个数据集都无法回答的问题。
因果模型可以帮助解决外部有效性问题(一项研究的结果是否适用于未研究的总体)。因果模型可以允许多个研究的数据(在某些情况下)合并来回答任何单个数据集都无法回答的问题。
因果模型是可证伪的，因为如果它们与数据不匹配，它们就必须作为无效模型而被拒绝。它们还必须使得接触模型所要解释现象的群体信赖它们。
因果模型是可证伪的，因为如果它们与数据不匹配，它们就必须作为无效模型而被拒绝。它们还必须使得接触模型所要解释现象的群体信赖它们。
因果模型在信号处理、流行病学和机器学习中都有应用。
因果模型在信号处理、流行病学和机器学习中都有应用。
== Definition ==
== 定义 ==
<blockquote>Causal models are mathematical models representing causal relationships within an individual system or population. They facilitate inferences about causal relationships from statistical data. They can teach us a good deal about the epistemology of causation, and about the relationship between causation and probability. They have also been applied to topics of interest to philosophers, such as the logic of counterfactuals, decision theory, and the analysis of actual causation.<ref>{{Citation|last=Hitchcock|first=Christopher|title=Causal Models|date=2018|url=https://plato.stanford.edu/archives/fall2018/entries/causal-models/|encyclopedia=The Stanford Encyclopedia of Philosophy|editor-last=Zalta|editor-first=Edward N.|edition=Fall 2018|publisher=Metaphysics Research Lab, Stanford University|access-date=2018-09-08}}</ref></blockquote>
<blockquote>Causal models are mathematical models representing causal relationships within an individual system or population. They facilitate inferences about causal relationships from statistical data. They can teach us a good deal about the epistemology of causation, and about the relationship between causation and probability. They have also been applied to topics of interest to philosophers, such as the logic of counterfactuals, decision theory, and the analysis of actual causation.<ref>{{Citation|last=Hitchcock|first=Christopher|title=Causal Models|date=2018|url=https://plato.stanford.edu/archives/fall2018/entries/causal-models/|encyclopedia=The Stanford Encyclopedia of Philosophy|editor-last=Zalta|editor-first=Edward N.|edition=Fall 2018|publisher=Metaphysics Research Lab, Stanford University|access-date=2018-09-08}}</ref></blockquote>
Judea Pearl 将因果模型定义为一个有序的三元组<math>\langle U, V, E\rangle</math> ，其中 U 是一组外生变量，其值由模型外部的因素决定; V 是一组内生变量，其值由模型内部的因素决定; E 是一组结构方程，把每个内生变量的值表示为 U 和 V 中其他变量值的函数。
Judea Pearl 将因果模型定义为一个有序的三元组<math>\langle U, V, E\rangle</math> ，其中 U 是一组外生变量，其值由模型外部的因素决定; V 是一组内生变量，其值由模型内部的因素决定; E 是一组结构方程，把每个内生变量的值表示为 U 和 V 中其他变量值的函数。
== History ==
== 历史 ==
亚里士多德定义了因果关系的分类法，包括质料因、形式因、动力因、目的因。休谟更偏爱反事实，他拒绝了亚里士多德的分类法。有段时间，他否认物体本身具有使得一个物体成为原因而另一个物体成为结果的“力量”。后来，他接受了“第一物体还没存在时，第二个根本不存在”的观点（“but-for”因果关系）。
19世纪末，统计学学科开始形成。经过多年努力确定诸如生物遗传等领域的因果规则后，高尔顿引入了均值回归的概念（以二年生症候群为缩影），后来这将他引向了非因果的相关性概念。
作为一个实证主义者，皮尔逊将因果的概念从许多科学中去除，他认为因果关系是一种无法证明的特殊的关联，并引入相关系数作为关联强度的度量方法。他写道: “作为运动原因的力，与作为成长原因的树神完全一样”，而因果关系只是“现代科学高深奥秘中的迷信”。皮尔逊在伦敦大学学院创立了“Biometrika”和生物识别实验室，该实验室成为了统计领域的全球领导者。
1908年，Hardy和Weinberg通过重拾孟德尔遗传律，解决了导致高尔顿放弃因果关系的性状稳定问题。
1921年，Wright的路径分析成为因果模型和因果图的理论雏形。他开发了这种路径分析方法，试图同时阐明遗传、发育和环境对豚鼠皮毛模式的相对影响。他通过展示这样的分析如何解释豚鼠出生体重、子宫内时间和产仔数之间的关系来支持他旁门左道的观点。杰出的统计学家对这些想法的反对使因果关系在接下来的40年中被忽略（除了动物饲养员）。取而代之的是，科学家依赖于相关性，<font color="#32cd32"> partly at the behest of Wright's critic (and leading statistician), Fisher</font>。唯一的例外是一名叫Burks的学生，在1926年首先应用路径图来表示中介影响，并断言保持中介变量恒定会引起误差。她可能独立地发明了路径图。
1923年，Neyman提出了潜在结果(potential outcome)的概念，但是直到1990年他的论文才从波兰语被翻译成英语。
1958年，Cox警告说，控制一个变量Z仅在Z高概率不受到自变量影响的情况下才有效。
19世纪60年代，Duncan、Blalock、Goldberger等人重新发现了路径分析。Duncan在阅读Blalock关于路径图的著作时，想起了二十年前Ogburn的一次演讲，其中提到了Wright的论文，而后又提到了Burks。
社会学家最初将因果模型称为结构方程模型，但一旦它成为教条式方法就失去了效用，导致一些从业者拒绝与因果关系的任何联系。经济学家采用了路径分析的代数部分，称其为联立方程建模。但是，经济学家仍然避免将因果含义赋予他们的方程式。
Wright在发表第一篇论文60年后，根据Karlin等人的批评，发表了一篇概述该论文的文章，该论文反对仅处理线性关系，而鲁棒的、非模型的数据表示方式则更具揭示性。
1973年，Lewis提倡用but-for因果关系（反事实）代替相关性。他提到了<font color="#32cd32"> humans' ability to envision alternative worlds in which a cause did or not occur and in which effect an appeared only following its cause </font>。1974年Rubin引入了“潜在结果”（potential outcome）的概念，作为询问因果问题的语言。
1983年，Cartwright提出<font color="#32cd32">any factor that is "causally relevant" to an effect be conditioned on, moving beyond simple probability as the only guide</font>。
1986年，Baron和Kenny引入了检测和评估线性方程系统中的中介的原理。截至2014年，他们的论文在所有时间中被引用次数排在第33位。那年，Greenland和Robins通过考虑反事实，引入了“可交换性”方法，来处理混杂问题。他们提出评估如果治疗组没有接受治疗会给治疗组带来什么后果，并将其结果与对照组进行比较。如果结果一致，说明没有混杂因子。
哥伦比亚大学设有因果人工智能实验室，该实验室正试图将因果建模理论与人工神经网络联系起来。
== 因果关系之梯 ==
Pearl的因果元模型涉及三个层次的抽象，他称之为因果之梯。最低层的“关联”（看到/观察）需要感知输入数据中的规律性或模式，用相关性表示。中间层的“干预”（做）可以预测有意识行动的后果，用因果关系表示。最高层的“反事实”（想象）涉及构建部分世界的理论，该理论解释为什么特定行为会产生特定后果，以及在没有此行为的情况下会发生什么。
=== 关联 ===
:<math>P(Y|do(X)) = \textstyle \sum_{z} \displaystyle P(Y|X, Z=z) P(Z=z)</math>
如果观察一个对象改变了观察另一个对象的可能性，则这个对象与另一个对象相关联。例子：购买牙膏的购物者也更有可能购买牙线。数学上用
:<math>P (牙线 | 牙膏) </math>
表示已知一个人购买牙膏时的其购买牙线的可能性。关联也可以通过计算两个事件的相关性来测量。关联没有因果含义。一个事件可能导致另一个事件，反过来也可能，或者两个事件都可能由某个第三事件引起（卫生学家使得购物者购买牙线和牙膏）。
=== 干预 ===
该层涉及事件之间的特定因果关系。因果是通过实验性地执行影响事件的一些动作来评估。例子：如果我们将牙膏的价格提高一倍，那么人们购买牙线的概率将是多少？因果无法通过检验（价格变化）历史来确定，因为可能存在其他因素同时影响这两个变量，比如存在牙膏价格变化的其他原因，而且这种原因会影响牙线的价格（两种商品的关税增加）。数学上用
:<math>P (牙线 | do(牙膏)) </math>
表示这种概率。其中do是一个算子，表示对谁做实验性干预（如价格翻倍）。这个算子指示了要在创造所需效果的世界中进行最小的变化，即在现实模型上进行尽可能小的改变的“小手术”。
=== 反事实 ===
最高层的反事实涉及对过去事件的其他可能版本的考虑，或者考虑同一实验单位中在不同情况下会发生的情况。例如，如果当初那家商店的牙线价格翻了一番，那么当时那些购买牙膏的购物者仍然会购买牙线的可能性是多少？
:<math>P (牙线 | 牙膏, 牙线价格翻倍) </math>
反事实可以表明存在因果关系。可以回答反事实的模型允许进行精确的后果可以预测的干预。在极致情况下，这样的模型被作为物理定律（如若不将力施加到静止物体上物体将不会移动的惯性）。
== 因果 ==
== Ladder of causation ==
=== 因果和关联 ===
统计学设计分析多个变量之间的关系。传统上，这些关系被描述为相关性，即没有任何隐含因果关系的关联。因果模型试图通过添加因果关系的概念来扩展此框架，在因果关系中，一个变量的变化导致其他变量的变化。
二十世纪因果的定义完全依赖于概率/关联。一个事件 X 如果增加了另一个事件 Y 的可能性，则认为它会导致另一个事件。在数学上，这表示为：
:<math>P (Y | X) > P(Y)</math>
这样的定义是不充分的，因为可能有其他关系（例如，X和Y的常见原因）可以满足该条件。因果与因果之梯的第二层有关。关联处于第一层，仅向第二层提供证据。
之后的定义试图通过以背景因素为条件来解决这种歧义。数学上：
:<math>P (Y | X, K = k) > P(Y| K = k)</math>
其中K是背景变量的集合，k表示特定语境中背景变量的值。但是，所需的背景变量集是难以确定的。
定义因果的其他尝试包括格兰杰因果，这是一种统计假设检验，在经济学中可以通过测量用一个时间序列的过去值预测另一个时间序列的未来值的能力来评估序列间的因果。
=== 类型 ===
原因可以是必要的、充分的、部分的以及它们的组合。
==== 必要因 ====
对于 y 的必要因 x ，y的存在意味着 x在此前发生了。但是x的存在不意味着y会发生。必要因也被称为“若非”因，因为y不会发生若非 x 发生。
==== 充分因 ====
对于y的充分因x，x的存在意味着y接下来会发生。然而另一个原因z也可能独立地造成y的发生。即y的发生不要求x的发生。
==== 部分因 ====
对于y的部分因x，x的存在会增加y的似然。如果似然是100%，那么x就是充分的。部分因也是必要的。
=== 模型 ===
==== 因果图 ====
因果图是一个有向图，它显示了因果模型中变量间的因果关系。因果图包括一组变量（或节点）。每个节点通过箭头连接到一个或多个对其具有因果效应的其他节点。箭头描绘了因果的方向，例如，将变量A和B与位于B处的箭头相连的箭头表示A的变化导致B的变化（以某种概率）。一条路径是两个节点间沿着因果箭头的图的遍历。
因果图包括因果环图，有向无环图和Ishikawa图。
因果图和它们的定量概率无关。对这些概率的更改（例如，由于技术改进）不需要更改因果图。
==== 模型元素 ====
因果模型具有形式结构，其元素具有特定的属性。
=== Intervention ===
===== 结点模式 ======
三个节点的连接类型有三种，分别是线性链式，分支叉式和合并对撞式。[5]
===== 链 =====
链是直线连接，箭头指向因果关系。在这个模型中，B是中介者，因为它可以中介A否则会对C所做的更改。
:<math> A -> B -> C</math>
===== 叉 =====
在叉中，一个原因有多种结果。这两种结果有一个共同的原因。A和C之间存在（非因果的）虚假相关性，可以通过把B作为条件（选取B的特定值）来消除虚假相关性。
:<math> A <- B -> C</math>
“把B作为条件”是指“给定B”（即B取某个值）。
某些情况下叉是混杂因子：
:<math> A <- B -> C -> A</math>
在这样的模型中，B是A和C的共同原因（C也是A的原因），这使B成为混杂因子。
===== 对撞因子 =====
在对撞模式中，多种原因会影响一种结果。以B为条件（B取特定值）通常会揭示A与C之间的非因果的负相关。这种负相关被称为对撞偏差和“解释性”效应，即B解释了A与C之间的相关性。该相关性在A和C两者都是影响B的必要因时是正的。
:<math> A -> B <- C</math>
==== 节点类型 ====
===== 中介变量 =====
中介节点修改了其他原因对结果的影响（与原因简单地影响结果不同）。例如，在上面的链结构中，B是中介变量，因为它修改了A（C的间接原因）对C（结果）的影响。
===== 混杂因子 =====
混杂节点影响多个结果，从而在它们之间产生正相关。
===== 工具变量 =====
满足如下条件的是工具变量：
（1）有通往结果的路径
（2）没有通往其他因果变量的路径
（3）对结果没有直接影响
回归系数可以用作工具变量对结果的因果影响的估计，只要该影响不被混杂即可。通过这种方式，工具变量允许对因果因子进行量化，而无需有关混杂因子的数据。
例如，给定模型：
:<math> Z -> X -> Y <- U -> X</math>
Z是一种工具变量，因为它有一条通往结果Y的路径，并且不受U的混杂。
===== 孟德尔随机化 =====
定义：孟德尔随机化使用已知功能的基因来观察研究中可改变的部分对疾病的因果关系。
由于基因在人群中随机变化，因此基因的存在通常可以视为工具变量，这意味着在许多情况下，可以使用观察性研究中的回归来量化因果关系。
Category:Causal diagrams
Category:Causal diagrams
分类: 因果关系
分类: 因果关系
Category:Formal epistemology
Category:Formal epistemology
范畴: 形式认识论
范畴: 形式认识论