The Annals of Statistics

Minimal sufficient causation and directed acyclic graphs

Tyler J. VanderWeele and James M. Robins

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Abstract

Notions of minimal sufficient causation are incorporated within the directed acyclic graph causal framework. Doing so allows for the graphical representation of sufficient causes and minimal sufficient causes on causal directed acyclic graphs while maintaining all of the properties of causal directed acyclic graphs. This in turn provides a clear theoretical link between two major conceptualizations of causality: one counterfactual-based and the other based on a more mechanistic understanding of causation. The theory developed can be used to draw conclusions about the sign of the conditional covariances among variables.

Article information

Source
Ann. Statist., Volume 37, Number 3 (2009), 1437-1465.

Dates
First available in Project Euclid: 10 April 2009

Permanent link to this document
https://projecteuclid.org/euclid.aos/1239369027

Digital Object Identifier
doi:10.1214/08-AOS613

Mathematical Reviews number (MathSciNet)
MR2509079

Zentralblatt MATH identifier
1160.62003

Subjects
Primary: 62A01: Foundations and philosophical topics 62M45: Neural nets and related approaches
Secondary: 62G99: None of the above, but in this section 68T30: Knowledge representation 68R10: Graph theory (including graph drawing) [See also 05Cxx, 90B10, 90B35, 90C35] 05C20: Directed graphs (digraphs), tournaments

Keywords
Causal inference conditional independence directed acyclic graphs graphical models interactions sufficient causation synergism

Citation

VanderWeele, Tyler J.; Robins, James M. Minimal sufficient causation and directed acyclic graphs. Ann. Statist. 37 (2009), no. 3, 1437--1465. doi:10.1214/08-AOS613. https://projecteuclid.org/euclid.aos/1239369027


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