Journal
ANNALS OF STATISTICS
Volume 45, Issue 6, Pages 2618-2653Publisher
INST MATHEMATICAL STATISTICS
DOI: 10.1214/16-AOS1537
Keywords
Conditional independence; extended conditional independence; sufficiency; ancillarity; causality; separoid
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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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