The Annals of Statistics

A generalized back-door criterion

Marloes H. Maathuis and Diego Colombo

Full-text: Open access

Abstract

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.

Article information

Source
Ann. Statist., Volume 43, Number 3 (2015), 1060-1088.

Dates
Received: July 2013
Revised: November 2014
First available in Project Euclid: 15 May 2015

Permanent link to this document
https://projecteuclid.org/euclid.aos/1431695638

Digital Object Identifier
doi:10.1214/14-AOS1295

Mathematical Reviews number (MathSciNet)
MR3346697

Zentralblatt MATH identifier
1320.62157

Subjects
Primary: 62H99: None of the above, but in this section

Keywords
Causal inference covariate adjustment hidden confounders DAG CPDAG MAG PAG

Citation

Maathuis, Marloes H.; Colombo, Diego. A generalized back-door criterion. Ann. Statist. 43 (2015), no. 3, 1060--1088. doi:10.1214/14-AOS1295. https://projecteuclid.org/euclid.aos/1431695638


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