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

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.