Open Access
June 2009 Minimal sufficient causation and directed acyclic graphs
Tyler J. VanderWeele, James M. Robins
Ann. Statist. 37(3): 1437-1465 (June 2009). DOI: 10.1214/08-AOS613


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.


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Tyler J. VanderWeele. James M. Robins. "Minimal sufficient causation and directed acyclic graphs." Ann. Statist. 37 (3) 1437 - 1465, June 2009.


Published: June 2009
First available in Project Euclid: 10 April 2009

zbMATH: 1160.62003
MathSciNet: MR2509079
Digital Object Identifier: 10.1214/08-AOS613

Primary: 62A01 , 62M45
Secondary: 05C20‎ , 62G99 , 68R10 , 68T30

Keywords: Causal inference , Conditional independence , directed acyclic graphs , graphical models , interactions , sufficient causation , synergism

Rights: Copyright © 2009 Institute of Mathematical Statistics

Vol.37 • No. 3 • June 2009
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