We present a basis for studying questions of cause and effect in statistics which subsumes and reconciles the models proposed by Pearl, Robins, Rubin and others, and which, as far as mathematical notions and notation are concerned, is entirely conventional. In particular, we show that, contrary to what several authors had thought, standard probability can be used to treat problems that involve notions of causality, and in a way not essentially different from the way it has been used in the area generally known (since the 1960s, at least) as 'applied probability'. Conventional, elementary proofs are given of some of the most important results obtained by the various schools of 'statistical causality', and a variety of examples considered by those schools are worked out in detail. Pearl's 'calculus of intervention' is examined anew, and its first two rules are formulated and proved by means of elementary probability for the first time since they were stated 25 years or so ago. Note: Corrected and extended parts of this paper will soon be published as a book of the same title.
翻译:本文提出了一个研究统计学中因果问题的框架,该框架涵盖并协调了Pearl、Robins、Rubin等人提出的模型,且在数学概念与符号表示上完全遵循常规。特别地,我们证明:与部分学者此前观点相反,标准概率论可用于处理涉及因果概念的问题,且其应用方式本质上与(至少自20世纪60年代以来)被称为"应用概率"领域中传统使用的概率方法无异。我们以常规初等概率论的方法,对多派"统计因果性"学派所取得的重要成果给出了证明,并详细解析了这些学派所考察的各类案例。本文重新审视了Pearl的"干预演算"体系,首次在其提出约25年后,采用初等概率论方法表述并证明了该系统前两条规则。注:本文经修正与扩展的内容即将以同名专著形式出版。