Titel_SS06

accordance with requirements and well documented. The second fact being that two different
construction teams were involved in the execution of the two different bridges.

Having revealed this information you are of course still not too happy about the condition of
the bridge but anyhow relieved that probably only one bridge has problems.

The above story may be formalised by letting the condition of the two bridges be represented
by two states, namely good and bad. Furthermore the states are associated with uncertainty.
There are altogether four variables of interest in the present example, namely the condition of
the two bridges, the production records and the execution, see Figure 10.1.

Execution Production

Bridge 1 Bridge 2

Figure 10.1: Illustration of the causal interrelation between the execution and production and the
quality of the two bridges.

The present small example illustrates how dependence changes with the available information
at hand. When nothing is known about the concrete production and the quality of the
execution the conditions of the two bridges are dependent. On the other hand as information
becomes available the dependency is changed (reduced), meaning that information about one
bridge does not transfer to the other bridge, the conditions of the two bridges become
conditional independent.

Assume now that in order to increase the certainty about the reason for the poor quality of
bridge 1 you decide to inspect bridge 2 and find that bridge two is in perfect condition. This
information immediately increases your suspicion that the performance of the construction
team having executed bridge 1 is substandard and you consider whether you should fire them
or just increase the supervision on their team.

This last development in the example shows an interesting aspect, something, which is easy
for the human mind but difficult for machines, namely what is referred to as explaining away.

Furthermore the example shows that the causality goes in the direction of the links between
the states in the network whereas the reasoning goes in the opposite direction. It is the latter
situation which is the more delicate one and which will be reverted to a little later.

10.3 Introduction to Causal and Bayesian Networks

A causal network is formally speaking a set of variables and a set of directed links or edges,
between the variables representing uncertain events. Mathematically speaking the network is