**Analysing a BBN: entering evidence and propagation
**
Having entered the probabilities we can now use Bayesian probability to do
various types of analysis. For example, we might want to calculate the
(unconditional) probability that Norman is late:
p(Norman late) = p(Norman late | train strike) * p(train strike) + p(Norman
late | no train strike)
= (0.8 * 0.1) + (0.1 * 0.9) = 0.17
This is called the marginal probability (see Section 8.4).
Similarly, we can calculate the marginal probability that Martin is late to be
0.51.
However, the most important use of BBNs is in *revising* probabilities in the light of actual observations of events. Suppose, for
example, that we *know* there is a train strike. In this case we can **enter the evidence **that 'train strike' = true. The conditional probability tables already tell us
the revised probabilities for Norman being late (0.8) and Martin being late
(0.6). Suppose, however, that we do not know if there is a train strike but do
know that Norman is late. Then we can enter the evidence that 'Norman late' =
true and we can use this observation to determine:
a) the (revised) probability that there is a train strike; and
b) the (revised) probability that Martin will be late.
To calculate a) we use Bayes theorem :
Thus, the observation that Norman is late significantly increases the
probability that there is a train strike (up from 0.1 to 0.47). Moreover, we can use
this revised probability to calculate b):
p(Martin late) = p(Martin late | train strike) * p(train strike) + p(Martin
late | no train strike)
= (0.6 * 0.47) + (0.5 * 0.53) = 0.55
Thus, the observation that Norman is late has slightly increased the
probability that Martin is late. When we enter evidence and use it to update the
probabilities in this way we call it **propagation**.
For a detailed look at how BBNs transmit evidence for propagation (including
the notions of *d-connectedness* and *separation*) click here .
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