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Causality, Conditional Independence, and Graphical Separation in Settable Systems

  • Karim Chalak

    ()

    (Boston College)

  • Halbert White

    (University of California-San Diego)

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 sufficient 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.

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Paper provided by Boston College Department of Economics in its series Boston College Working Papers in Economics with number 689.

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Date of creation: 11 Sep 2008
Date of revision: 04 Jul 2010
Handle: RePEc:boc:bocoec:689
Note: Previously circulated as "Independence and Conditional Independence in Causal Systems"
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Web page: http://fmwww.bc.edu/EC/
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  1. Karim Chalak & Halbert White, 2007. "An Extended Class of Instrumental Variables for the Estimation of Causal Effects," Boston College Working Papers in Economics 692, Boston College Department of Economics, revised 30 Nov 2009.
  2. Donald B. Rubin, 2004. "Direct and Indirect Causal Effects via Potential Outcomes," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 31(2), pages 161-170.
  3. Steffen L. Lauritzen & Thomas S. Richardson, 2002. "Chain graph models and their causal interpretations," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 64(3), pages 321-348.
  4. Sims, Christopher A, 1972. "Money, Income, and Causality," American Economic Review, American Economic Association, vol. 62(4), pages 540-52, September.
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