EXAMPLE

To illustrate the results and algorithms described previously, a simple example is discussed in this section. This example is based on the example described by Charniak [5] and on the calculations presented by Walley [28, Section 9.3.4].

Consider the graph in Figure 1. There are five binary variables in the graph (the superscript c indicates negation). These relationships are summarized by the probabilistic model presented in Figure 1. Note that the probabilities for f and b are not specified exactly; instead, they are given as an interval [0.4, 0.5]. The question is how to evaluate the impact of this imprecision in probability values. To illustrate the various algorithms discussed in the paper, consider the calculation of $\underline{p}\left( d\vert l \right)$ and $\overline{p}\left( d\vert l \right)$.

Figure: Example network (graphical structure and probabilistic statements).