Open Access
December 2017 Extended conditional independence and applications in causal inference
Panayiota Constantinou, A. Philip Dawid
Ann. Statist. 45(6): 2618-2653 (December 2017). DOI: 10.1214/16-AOS1537


The goal of this paper is to integrate the notions of stochastic conditional independence and variation conditional independence under a more general notion of extended conditional independence. We show that under appropriate assumptions the calculus that applies for the two cases separately (axioms of a separoid) still applies for the extended case. These results provide a rigorous basis for a wide range of statistical concepts, including ancillarity and sufficiency, and, in particular, the Decision Theoretic framework for statistical causality, which uses the language and calculus of conditional independence in order to express causal properties and make causal inferences.


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Panayiota Constantinou. A. Philip Dawid. "Extended conditional independence and applications in causal inference." Ann. Statist. 45 (6) 2618 - 2653, December 2017.


Received: 1 December 2015; Revised: 1 December 2016; Published: December 2017
First available in Project Euclid: 15 December 2017

zbMATH: 06838145
MathSciNet: MR3737904
Digital Object Identifier: 10.1214/16-AOS1537

Primary: 62A99
Secondary: 60A05

Keywords: ancillarity , causality , Conditional independence , extended conditional independence , separoid , sufficiency

Rights: Copyright © 2017 Institute of Mathematical Statistics

Vol.45 • No. 6 • December 2017
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