252
个编辑
更改
→实例4 - 辛普森悖论
\begin{equation}
\begin{equation}
P(Y=1|do(X=1)) = \sum_Z P(Y=1|X=1, Z=z)P(Z) = P(Y=1|X=1, Z=1)P(Z=1) + P(Y=1|X=1, Z=0)P(Z=0)
P(Y=1|do(X=1))= \sum_Z P(Y=1|X=1, Z=z)P(Z) = P(Y=1|X=1, Z=1)P(Z=1) + P(Y=1|X=1, Z=0)P(Z=0)
= \frac{0.93*(87+270)}{700} + \frac{0.73*(263+80)}{700} = 0.832
\end{equation}
\end{equation}