The notion of 'explaining away' evidence
Now consider the following slightly more complex network:
In this case we have to construct a new conditional probability table for node
B ('Martin late') to reflect the fact that it is conditional on two parent nodes (A and D). Suppose the table is:

 Martin oversleeps
 True

 False



 Train strike
 True
 False
 True
 False

Martin late

 True

 0.8
 0.5
 0.6
 0.5

We also have to provide a probability table for the new root node D ('Martin
oversleeps').
Martin oversleeps


True
 0.4

False
 0.6

We have already seen that in this initialised state the probability that
Martin is late is 0.51 and the probability that Norman is late is 0.17.
Suppose we find out that Martin is late. This evidence increases our belief in both of the possible causes
(namely a train strike A and Martin oversleeping B). Specifically, applying Bayes
theorem yields a revised probability of A of 0.13 (up from the prior probability
of 0.1) and a revised probability of D of 0.41 (up from the prior probability
of 0.4). However, if we had to bet on it, our money would be firmly on Martin
oversleeping as the more likely cause. Now suppose we also discover that Norman
is late. Entering this evidence and applying Bayes yields a revised probability
of 0.54 for a train strike and 0.44 for Martin oversleeping. Thus the odds are
that the train strike, rather than oversleeping, have caused Martin to be late.
We say that Martin's lateness has been 'explained away'.