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I understand backdoor adjustment blocks backdoor paths and front door adjustment combines the causal effect of different nodes. The purpose of both is to eventually identify the causal effect of a treatment on the outcome variable.

How do the 3 rules of do-calculus help in doing the same?

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    $\begingroup$ There are some situations where it is not possible to use backdoor, frontdoor, etc., but it is possible to use do-calculus. Indeed, do-calculus has been proved to be sufficient: if a causal effect is identifiable at all, do-calculus can be used to prove it. $\endgroup$
    – Adrian Keister
    Commented Nov 19, 2021 at 18:45

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What's the purpose of do-calculus?

The do-calculus is an axiomatic system for replacing probability formulas containing the do operator with ordinary conditional probabilities.

Criterions like backdoor and frontdoor can be considered as consequence of do-calculus. Them are verifiable under some conditions. However, as suggested by Adrian Keister, those conditions sometimes do not holds.

Read here for more details: https://plato.stanford.edu/entries/causal-models/do-calculus.html

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  • $\begingroup$ How can we replace probability formulas containing do operator with ordinary conditional probabilities? From my understanding, all three do-calculus rules have do- operators on the left and right hand side. $\endgroup$
    – desert_ranger
    Commented Nov 20, 2021 at 17:25
  • $\begingroup$ All depends on the causal model at hands. However, in general, you have to use the rules repeatedly. Do operator disappear at the end of the story, and not always. Note that all math rules work in similar way. $\endgroup$
    – markowitz
    Commented Nov 20, 2021 at 19:41

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