Independence and Conditional Independence in Causal Systems

Karim Chalak () and Halbert White

No 689, Boston College Working Papers in Economics from Boston College Department of Economics

Abstract: We study the interrelations between (conditional) independence and causal relations in settable systems. We provide definitions in terms of functional dependence for direct, indirect, and total causality as well as for (indirect) causality via and exclusive of a set of variables. We then provide necessary and su¢ cient causal and stochastic conditions for (conditional) dependence among random vectors of interest in settable systems. Immediate corollaries ensure the validity of Reichenbach's principle of common cause and its informative extension, the conditional Reichenbach principle of common cause. We relate our results to notions of d-separation and D-separation in the artificial intelligence literature.

Keywords: causality; conditional independence; d-separation; direct effect; Reichenbach principle; settable systems (search for similar items in EconPapers)
JEL-codes: C10 C30 C31 C50 (search for similar items in EconPapers)
New Economics Papers: this item is included in nep-ecm
Date: 2008-09-11
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Persistent link: http://EconPapers.repec.org/RePEc:boc:bocoec:689

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