How does the 'do-calculus' help in causal inference?

Instruction: Explain the concept of do-calculus and its application in determining causal effects from observational data.

Context: This question assesses the candidate's knowledge of advanced techniques like do-calculus developed by Judea Pearl, which are used to derive causal relationships from data where traditional methods fall short.

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The do-operator distinguishes intervention from observation. P(Y | do(A=a)) describes setting A to a, whereas P(Y | A=a) conditions on how A arose naturally. These distributions need not be equal when treatment is confounded.

Do-calculus provides three graphical transformation rules: insertion/deletion of observations, exchange of actions and observations, and insertion/deletion of actions...

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