Examples of probabilistic graphical models

In this last section we will show several examples of PGM that are good candidates for exact inference. The goal of this section is to show realistic yet simple examples of what can be done and to provide the reader with ideas for developing his or her own models.

The sprinkler example

This is an historical example which has been used in many textbooks. It is rather simple and shows a simple reasoning.

Let's say we look at our garden and see the grass is wet. We want to know why the grass is wet. There are two possibilities: either it was raining before or we forgot to turn off the sprinkler. Moreover, we can observe the sky. If it's cloudy, chances are it was raining before. However, if it was cloudy then presumably we didn't turn on the sprinkler, so it is more likely, in this case, we would have not forgotten to turn off the sprinkler.

This is a little example of causal reasoning that can be represented by a PGM. We identify four...