Do operator: Difference between revisions

Revision as of 23:32, 23 September 2018

The do operator is used in causal inference to denote an intervention. Given random variables $X, Y$ , we write $Pr (Y = y ∣ d o (X = x))$ to mean the probability that $Y = y$ given we intervene and set $X$ to be $x$ . In some texts, this is abbreviated to $Pr (y ∣ \hat{x})$ (this notation assumes that the random variables corresponding to the individual values are clear from context). The notation ${Pr}_{x} (y)$ is also used.

In general $Pr (Y = y ∣ d o (X = x))$ is not the same as conditioning on $X = x$ , i.e. $Pr (Y = y ∣ X = x)$ .

The do operator is used extensively in the do calculus.

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-The '''''do'' operator''' is used in causal inference to denote an intervention. Given [[random variable]]s <math>X,Y</math>, we write <math>\Pr(Y=y \mid \mathit{do}(X=x))</math> to mean the [[probability]] that <math>Y=y</math> given we intervene and set <math>X</math> to be <math>x</math>. In some texts, this is abbreviated to <math>\Pr(y\mid\hat x)</math> (this notation assumes that the random variables corresponding to the individual values are clear from context).
+The '''''do'' operator''' is used in causal inference to denote an intervention. Given [[random variable]]s <math>X,Y</math>, we write <math>\Pr(Y=y \mid \mathit{do}(X=x))</math> to mean the [[probability]] that <math>Y=y</math> given we intervene and set <math>X</math> to be <math>x</math>. In some texts, this is abbreviated to <math>\Pr(y\mid\hat x)</math> (this notation assumes that the random variables corresponding to the individual values are clear from context). The notation <math>\Pr_x(y)</math> is also used.
 In general <math>\Pr(Y=y \mid \mathit{do}(X=x))</math> is not the same as conditioning on <math>X=x</math>, i.e. <math>\Pr(Y=y \mid X=x)</math>.
 The ''do'' operator is used extensively in the [[Do calculus|''do'' calculus]].