Do operator

The do operator is used in causal inference to denote an intervention. Given random variables $X,Y$, we write $Pr(Y=y\mid \mathit{d}\mathit{o}(X=x))$ to mean the probability that $Y=y$ given we intervene and set $X$ to be $x$. In some texts, this is abbreviated to $Pr(y\mid \hat{x})$.

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