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  • The following topics will be covered in this lecture:
    • Discussion of causality
    • The notion of statistical explanation
    • Confounding variables and covariates


  • We have now explored the notion of a predictive model, but the notion of an explanatory model is more complicated philosophically.

  • Sometimes explanation means causation by physical principles,

    • E.g., if we fit a linear model for a physical application, a paramater \( \beta \) might be physical constant;
    • in particular, it could represent the ammount of energy lost due to friction in the moving parts of machine.
  • However, sometimes explanation is just a description of the (conditional/ stastical) relationships between the variables.

  • Causal conclusions require stronger assumptions than those used for the predictive models that we have already discussed.

  • Sometimes, we only wish to understand correlations, i.e., variables that (co)-vary together or asymmetrically…

Correlation models

  • … but sometimes we can't read much into correlation: