## Annals of Statistics

- Ann. Statist.
- Volume 45, Number 6 (2017), 2618-2653.

### Extended conditional independence and applications in causal inference

Panayiota Constantinou and A. Philip Dawid

#### Abstract

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.

#### Article information

**Source**

Ann. Statist., Volume 45, Number 6 (2017), 2618-2653.

**Dates**

Received: December 2015

Revised: December 2016

First available in Project Euclid: 15 December 2017

**Permanent link to this document**

https://projecteuclid.org/euclid.aos/1513328585

**Digital Object Identifier**

doi:10.1214/16-AOS1537

**Mathematical Reviews number (MathSciNet)**

MR3737904

**Zentralblatt MATH identifier**

06838145

**Subjects**

Primary: 62A99: None of the above, but in this section

Secondary: 60A05: Axioms; other general questions

**Keywords**

Conditional independence extended conditional independence sufficiency ancillarity causality separoid

#### Citation

Constantinou, Panayiota; Dawid, A. Philip. Extended conditional independence and applications in causal inference. Ann. Statist. 45 (2017), no. 6, 2618--2653. doi:10.1214/16-AOS1537. https://projecteuclid.org/euclid.aos/1513328585

#### Supplemental materials

- Some Proofs. Supplementary material, comprising proofs of Lemma 2.2, Theorem 2.4, Proposition 2.5, Proposition 2.6, Theorem 2.7, Proposition 3.1, Theorem 4.2 and Theorem 4.3, is available online.Digital Object Identifier: doi:10.1214/16-AOS1537SUPPSupplemental files are immediately available to subscribers. Non-subscribers gain access to supplemental files with the purchase of the article.