> For the complete documentation index, see [llms.txt](https://json007.gitbook.io/svm/llms.txt). Markdown versions of documentation pages are available by appending `.md` to page URLs; this page is available as [Markdown](https://json007.gitbook.io/svm/bayes/bayesian_network.md).

# bayesian network

[D分离](https://mqshen.gitbooks.io/prml/content/Chapter8/conditional/three_example_graphs.html)

![](/files/-M7DeR3hB_8JCbcShi89)

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

![](/files/-M7DeR3iVGmOPVMpLdek)

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

![](/files/-M7DeR3jqDH1WIU8cAV6)

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

此结构与前两个不同，当C被观测，a和b却相互影响。