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.
翻译:我们为研究统计中的因果关系问题提供了基础,这些统计包含并调和了珍珠、罗宾、鲁宾等提出的模型,就数学概念和注解而言,这些模型是完全传统的。 特别是,我们表明,与一些作者所认为的相反,标准概率可用于处理涉及因果关系概念的问题,其方式与一般人所知道的(至少自1960年代以来)“适用概率”领域所使用的方式并无本质上的不同。 传统是,对不同“统计因果关系”学校所取得的一些最重要的结果提供了基本证据,这些学校所考虑的各种例子也得到了详细研究。 珍珠的“干预量”重新得到审查,其头两条规则的制定和证明是自25年前发表以来第一次以基本概率方式进行的。