> 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)

![](https://2270971654-files.gitbook.io/~/files/v0/b/gitbook-legacy-files/o/assets%2F-M7DcNFhVrwIk3Tks_pB%2Fsync%2F1d6fda2bb54569df769e4816fa43d6e85082be54.png?generation=1589383932008214\&alt=media)

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

![](https://2270971654-files.gitbook.io/~/files/v0/b/gitbook-legacy-files/o/assets%2F-M7DcNFhVrwIk3Tks_pB%2Fsync%2F6db1d6e749704ea4a083ec880efb4aa099bfa1c0.png?generation=1589383931652604\&alt=media)

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

![](https://2270971654-files.gitbook.io/~/files/v0/b/gitbook-legacy-files/o/assets%2F-M7DcNFhVrwIk3Tks_pB%2Fsync%2F4123cc506f3e93cc90b8d08f2a5a249dd211589d.png?generation=1589383931841617\&alt=media)

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

此结构与前两个不同，当C被观测，a和b却相互影响。