Computation of Variables in a Bayesian Belief Network

Example 1

$$\mathrm{P}(e)=\sum _{d\in \mathcal{D}}\mathrm{P}(e\mid d)\cdot \underset{\mathrm{P}(d)}{\underbrace{\sum _{c\in \mathcal{C}}\sum _{a\in \mathcal{A}}\mathrm{P}(d\mid c,a)\cdot \mathrm{P}(a)\cdot \stackrel{\mathrm{P}(c)}{\overbrace{\sum _{b\in \mathcal{B}}\mathrm{P}(c\mid b)\cdot \mathrm{P}(b)}}}}$$

• Node A: $P(a)$
• Node B: $P(b)$
• Node C: $P(c)={\sum }_{b\in B}P(c|b)\cdot P(b)$
• Node D: $P(d)={\sum }_{a\in A}{\sum }_{c\in C}P(d|a,c)\cdot P(a)\cdot P(c)$
• Node E: $P(e)={\sum }_{d\in D}P(e|d)\cdot P(d)$

Example 2

• Specify the probability $\mathrm{P}(A,B,C,D,E)$ by using the single terms of the Bayesian belief network (hint: First reorder the terms!)
• Now let $C$ be an unknown and the probability for $D$ be inquired.Write down the probability $\mathrm{P}(D\mid A,B,E)$ by using the single terms of the Bayesian belief network.

Example 3

Given: $P(C)$ is unknown WRONG

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