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IlyaShpitser comments on Causality: a chapter by chapter review - Less Wrong
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So what are the pre-requisites for reading the book and not the lecture?
Any motivated undergrad in a technical field has enough background. If you want to read other folks in the field, they tend to be more statistical than Pearl (and thus in addition it's good to have basic stat). It helps to have taken at least one class with proofs in it.