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Causal Inference in Statistics: An Overview (Pearl, 2009)
According to Shalizi, Pearl makes a summary of everything he knows about causality
Editing the Gelman/Pearl Debate on Causality
Pointers to the relevant posts. Reading Gelman's posts on this made me realize that I have a lot of ground to cover before I even start understanding causality.
Minimal sufficient causation and directed acyclic graphs
Notions of minimal sufficient causation are incorporated within the directed acyclic graph causal framework. Doing so allows for the graphical representation of sufficient causes and minimal sufficient causes on causal directed acyclic graphs while maintaining all of the properties of causal directed acyclic graphs. This in turn provides a clear theoretical link between two major conceptualizations of causality: one counterfactual-based and the other based on a more mechanistic understanding of causation. The theory developed can be used to draw conclusions about the sign of the conditional covariances among variables.
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