# Markov blanket vs normal dependency in a Bayesian network

While I was reading about Bayesian networks, I run into "Markov blanket" term and got severely confused with its independency in a Bayesian network graph.

Markov blanket briefly says that every node is only dependent on its parents, children and children's parents [it is gray area for node A in the picture]. What is the joint probability of this BN, $$P(M,S,G,I,B,R)$$?

If I follow the step parent only independency rule, it is:

$$P(M | S)P(S | G,I)P(I | B)P(R | B)P(G)P(B)$$

However, if I follow the Markov Blanket independency, I end up with this (notice $$P(I|\mathbf{G},B)$$ is different):

$$P(M | S)P(S | G,I)P(I | \mathbf{G},B)P(R | B)P(G)P(B)$$

So which is the correct joint probability of this BN?

and

Respective chapter and diagrams are below:

alt text http://img828.imageshack.us/img828/9783/img0103s.png

alt text http://img406.imageshack.us/img406/3788/img0104l.png

• The links are all broken, could you please update them? – Lerner Zhang Jan 23 at 22:37