I'm currently trying to wrap my head around evidence propagation in bayesian network (simple tree propagation) but I'm having trouble finding information about the process.
As an example, let's take this graph from a set of slides.
The initialization of A and B is already done, C and D are now being initialized by B sending $\pi$-messages to them.
A $\pi$-message is computed like this
$\forall b \in \Omega_B : \pi_{B \rightarrow C}(b) = \frac{P'(b)}{\lambda_{C\rightarrow B }(b)}$
with reference to the $\lambda$-message that we get from
$\forall b \in \Omega_B : \lambda_{C\rightarrow B }(b)= \displaystyle\sum_{\forall c \in \Omega_C}^{} P(c|b)* \lambda (c) $
in this step it's still simple since the $\lambda$-value of B is 1, so the $\pi$-message is passed as shown.
Here the resulting P' and $\pi$-value differs from the other nodes tho, how did that happen? In general, how is the $\pi$-value computed based on an incoming $\pi$-message?
Now we receive evidence about C , telling us that $c_2$ happens. Because of this, the values for $c_2$ are set to 1.
How do we get the values of the $\lambda$-message that are shown here? How are they used to adjust the $\lambda$-value of the node above it?