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Notes of Causal Inference-3

2021-01-03
Zheng-Mao Zhu

Course Web

In note 1, we introduce the identification-estimation flowchart. And in note 2, we introduce the corresponding concepts in graphs.

Now we will introduce causal models and data into prior identification-estimation flowchart:

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The $do-$operator

Firstly we differ the conditioning and intervening:

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The main effect of introducing causal models is finding all the confounders $X$, by which we can have unconfounderness assumption and do identification:

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Modularity assumption

Nextly, we introduce the modularity assumption:

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More formaly:

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which means that

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Take a simple example of identifying $P(y \mid do(t))$:

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And then we can find the key difference between causation and association in formula:

image-1

which is the sample probability over the confounderness $X$.


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