It is this weakness that is both clarified and resolved in the following two new papers. However, it turns out that in situations where the child node (in the example this is the node “Attack carried out”) is observed to be “False”, the noisy-OR function fails to properly capture the real world implications. BN tools like AgenaRisk implement the noisy-OR function making it easy to define even very large probability tables. One of the most popular methods – “noisy-OR”- approximates the required relationship in many real-world situations like the above example.

Numerous methods have been proposed to simplify the problem of eliciting such probability tables. When there are more parents (imagine there are 20 different terrorist cells) or more states other than “False” and “True”, then it becomes practically infeasible. Even for a very small example like this, such elicitation is known to be highly error-prone. When data are sparse – as in examples like this – we must rely on judgment from domain experts to elicit these values. That is 16 values (although, since the columns must sum to one we only really have to define 8).

To define the probability table for the node “Attack carried out” we have to define probability values for each possible combination of the states of the parent nodes, i.e., for all the entries of the following table. In the case where there are three terrorist cells, it seems to reasonable to assume the BN structure here: The more cells known to have heightened activity the more likely an attack is. However, for any cell if it is known there is heightened activity then there is a chance an attack will take place. If it is known that there is no heightened activity in any of the cells, then an attack is unlikely. There are several independent cells in this organisation for which it may be possible in any week to determine heightened activity. In any given week a terrorist organisation may or may not carry out an attack.

One of the biggest practical challenges in building Bayesian network (BN) models for decision support and risk assessment is to define the probability tables for nodes with multiple parents.

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