Causality from the Point of View of Statistics

TL;DR

This paper develops a unified statistical framework for causality, demonstrating that standard probability can address causal questions and revisiting Pearl's intervention calculus with elementary proofs.

Contribution

It provides a conventional probability-based approach to causality, unifies different models, and offers elementary proofs of key results, including Pearl's calculus.

Findings

Standard probability suffices for causal reasoning

Elementary proofs of major causality results

Reformulation of Pearl's intervention rules

Abstract

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.