Sensitivity Analysis, Brushing History Sensitivity Analysis, Brushing History 
Figure 4. History browser showing parameter changes.
We can change the current active and base time points through the history browser. Figure 4 shows the history browser which is simply a log of every change made to the model. The primary selection (inverse video) is the active state and the secondary selection (blue dotted border) is the base state. With the mouse we can choose the state after our first parameter change as the new baseline. The probe now looks like Figure 5. It turns out that this was not a very big change after all. (The fourfold redundancy dimineshes the impact of the change.)
Figure 5. Probe with adjusted baseline.
With this example, we have learned how to use graphical belief to perform a simple sensitivity analysis. We simply relate our assumption to a variable or a parameter in the model. We change the value of that parameter and observe the change in predictions made by the model.
We also saw another important feature of Graphical-Belief, its object hierarchy. Even though the four pump-train systems fail independently, our knowledge about how the pump-train systems is not independent. In particular, we used the same parameter to represent the probability that any pump-train would fail even if none of its components fail. This is known as global dependence. This is an important difference between Graphical-Belief and most other graphical modelling software. The other packages only support global independence among the parameters. That means that in other software packages, you would need to make changes in four different places to do what we did with one change in Graphical-Belief. The situation could be much more complex, there could be many different instance of the same rule widely scattered throughout the graph, however, Graphical-Belief keeps track of them for you and lets you change them all with one change to the template parameter.
As another example of how this feature works, assume that a vendor has just contacted us and tells us they can sell us check-valves that cost half as much but are only half as reliable. How much reliability will we loose if we make the switch? Again, all we need to do is change the template "CV-Rule" and all six check valves in the model will change. However, we actually have test data for the check valves and other components. This is an example of a much more complex use of parameters in Graphical-Belief. The next example explores this idea.
Parameters and Data. Continue with this
example and explore how Graphical-Belief can
represent complex dependencies among probabilities using a parameter
network.
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