Single World Intervention Graphs as Distributions: A Framework for Causal Identification

TL;DR

This paper introduces a novel perspective on single-world intervention graphs (SWIGs), viewing them as representations of both observed and interventional distributions to facilitate causal effect identification.

Contribution

It provides a systematic approach to derive identifying expressions for causal effects using SWIGs, extending front-door criteria to complex settings.

Findings

Back-door derivations align with existing literature.

Front-door derivations offer new pathways for complex interventions.

The approach bridges Rubin's and Pearl's frameworks.

Abstract

Causal inference seeks to estimate the effect of an intervention on an outcome using observed data, typically via Rubin's potential-outcome framework or Pearl's do-calculus. Following section 9 of Richardson and Robins (2013), this essay treats single-world intervention graphs (SWIGs) as representations of both the observed-data distribution and the interventional distribution, rather than as a bridge to potential outcomes. We demonstrate that this perspective provides a systematic way to derive identifying expressions for estimands defined by interventions on selected variables. Back-door derivations mirror those in existing literature, while front-door derivations offer a distinct pathway that extends more readily to complex settings. Conceptually, the method is simultaneously related to and distinct from Rubin's framework and Pearl's calculus.