Let's take an example of four people who go out for dinner in different groups of two. A goes out with B, B goes out with C, C with D, and D with A. Due to some reasons (maybe due to a bad relationship), B doesn't want to go with D, and the same holds true for A and C. Let's think about the probability of them ordering food of the same cuisine. From our social experience, we know that people interacting with each other may influence each other's choice of food. In general, we can say that if A influences B's choice and B influences C's, then A might (as it is probabilistic) indirectly be influencing C's choice. However, given B's and D's choices, we can say with confidence that A won't affect C's choice of food. Formally, we can put this as . Similarly, as there is no direct interaction between A and C nor between B and D.

Let's try to model these independencies using a Bayesian network:

In the preceding figure, the one labeled Fig 2.1(a) is the Bayesian network...