bayesian network

D分离

\begin{eqnarray} p(a,b|c) &=& \frac{p(a,b,c)}{p(c)} \\ &=& \frac{p(a|c)p(b|c)p(c)}{p(c)} \\ &=& p(a|c)p(b|c) \end{eqnarray}

\begin{eqnarray} p(a,b|c) &=& \frac{p(a,b,c)}{p(c)} \\ &=& \frac{p(a)p(c|a)p(b|c)}{p(c)} \\ &=& p(a|c)p(b|c) \end{eqnarray}

\begin{eqnarray} p(a,b|c) &=& \frac{p(a,b,c)}{p(c)} \\ &=& \frac{p(a|c)p(b|c)p(c|a,b)}{p(c)} \end{eqnarray}

此结构与前两个不同，当C被观测，a和b却相互影响。