4. Compiling and Analyzing

Figure 11. Finishing the connections. The "Steam-Mov-Rule-1" icon is yellow because it inherits its probability distribution.

Compiling the model (Eliminating loops)

One of the things that Graphical-Belief does during compilation is eliminate loops (undirected cycles) in the graph. Loops cause the same kind of problems in graphical models as common parameter dependence. Unless we properly account for loops, we could produce similarly biased estimates. Graphical-Belief eliminates loops by building another representation of the model: the junction tree. The junction tree is a tree (hence it has no cycles) but its nodes contain multiple variables. Almond[1995] describes the tree of cliques an how to build it. Note that loops still add to the computation complexity: large loops often translate into large nodes in the tree of cliques which produce high computational cost.

When we talk about loops, we are referring to undirected cycles in the graph (i.e., not following the arrows). Directed cycles present a different kind of problem, one of model consistency. In the simplest situation, we are defining A conditioned on B and B conditioned on A. It is very difficult (and may not be possible) to produce a consistent model when there are directed cycles.

Once Graphical-Belief has compiled the model, we have our choice of views. The choices are (buttons along the graph window title bar in Figure 11):

• MC Model Construction: the view we have been using.
• DG Directed Graph: the view we have been using with for diagnosis.
• DH Directed Hypergraph: Similar to the model construction view but with colored nodes.
• JT Junction Tree: The junction tree.

Analyzing the results

Figure 12. Editing the Steam-Mov-Rule template to reflect the added risk from live steam.

Now we are ready to change the value of the MOV rule to represent the added failure risk with live steam. We open up a valuation editor on the template rule class "Steam-Mov-Rule". This will change both instances. Figure 12 shows the new rule.

Figure 13. Editing the Steam-Mov-Rule template to reflect the added risk from live steam.

Figure 13 shows the effect of this change. We can see that the failure probability has increased by 150%. Although this example is ficticious, it shows the importance of identifying potential common cause failures in modelling.

We have now completed the common cause failure analysis (although we could look at other conditional probabilities in the new model, the way we did in previous models). We have also explored Graphical-Belief's model construction capabilities. The object-oriented model construction which Graphical-Belief supports has some interesting implications in terms of storing knowledge. (Click here to return to that discussion.)

Return to the main example page.

Back to overview of Graphical-Belief.

View a list of Graphical-Belief in publications and downloadable technical reports.

The Graphical-Belief user interface is implemented in Garnet.

Get more information about obtaining Graphical-Belief (and why it is not generally available).

get the home page for Russell Almond , author of Graphical-Belief.

Click here to get to the home page for Insightful (the company that StatSci has eventually evolved into).