We learn a Bayes Net grphical structure by following Bayes rule:

\begin{align} P(G|D) &\propto P(D|G) P(G) \\ &= P(G) \int P(D | \theta, G) P(\theta|G) d\theta \\ &= P(G) \prod_{i=1}^{n} \prod_{j=1}^{q_{i}} \frac{\Gamma(\alpha_{i,j,0})}{\Gamma(\alpha_{i,j,0} + m_{i,j,0})} \prod_{k=1}^{r_{i}} \frac{\Gamma(\alpha_{i,j,k} + m_{i,j,k})}{\Gamma(\alpha_{i,j,k})} \end{align}

where, we define: \(\alpha_{i,j,0} = \sum_{k} \alpha_{i,j,k}\).

The actual integration process is not provided, but mostly uninteresting. See Beta Distribution for a flavour of how it came about.

This is hard. We are multiply many gammas together, which is computationally lame. So instead, we use

Goal: using protein-protein interfaces and docking to learn about the polymerase behavior

Too bio-y and I’m literally not sure how to make of it

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