Open Access
June 2015 A generalized back-door criterion
Marloes H. Maathuis, Diego Colombo
Ann. Statist. 43(3): 1060-1088 (June 2015). DOI: 10.1214/14-AOS1295


We generalize Pearl’s back-door criterion for directed acyclic graphs (DAGs) to more general types of graphs that describe Markov equivalence classes of DAGs and/or allow for arbitrarily many hidden variables. We also give easily checkable necessary and sufficient graphical criteria for the existence of a set of variables that satisfies our generalized back-door criterion, when considering a single intervention and a single outcome variable. Moreover, if such a set exists, we provide an explicit set that fulfills the criterion. We illustrate the results in several examples. R-code is available in the R-package pcalg.


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Marloes H. Maathuis. Diego Colombo. "A generalized back-door criterion." Ann. Statist. 43 (3) 1060 - 1088, June 2015.


Received: 1 July 2013; Revised: 1 November 2014; Published: June 2015
First available in Project Euclid: 15 May 2015

zbMATH: 1320.62157
MathSciNet: MR3346697
Digital Object Identifier: 10.1214/14-AOS1295

Primary: 62H99

Keywords: Causal inference , covariate adjustment , CPDAG , DAG , hidden confounders , MAG , PAG

Rights: Copyright © 2015 Institute of Mathematical Statistics

Vol.43 • No. 3 • June 2015
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