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When can statistical theories be causally closed?

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  • Gyenis, Balázs
  • Rédei, Miklós

Abstract

The notion of common cause closedness of a classical, Kolmogorovian probability space with respect to a causal independence relation between the random events is defined, and propositions are presented that characterize common cause closedness for specific probability spaces. It is proved in particular that no probability space with a finite number of random events can contain common causes of all the correlations it predicts; however, it is demonstrated that probability spaces even with a finite number of random events can be common cause closed with respect to a causal independence relation that is stronger than logical independence. Furthermore it is shown that infinite, atomless probability spaces are always common cause closed in the strongest possible sense. Open problems concerning common cause closedness are formulated and the results are interpreted from the perspective of Reichenbach's Common Cause Principle (RCCP).

Suggested Citation

  • Gyenis, Balázs & Rédei, Miklós, 2004. "When can statistical theories be causally closed?," LSE Research Online Documents on Economics 49733, London School of Economics and Political Science, LSE Library.
    • Handle: RePEc:ehl:lserod:49733
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    File URL: http://eprints.lse.ac.uk/49733/
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    References listed on IDEAS

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    1. Rédei, Miklós & Summers, Stephen J., 2002. "Local primitive causality and the common cause principle in quantum field theory," LSE Research Online Documents on Economics 49736, London School of Economics and Political Science, LSE Library.
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      Keywords

      probabilistic causation; Reichenbach's common cause principle;

      JEL classification:

      • C1 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General

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