In this chapter, we saw how we are not able to use a Bayesian model to model a problem in some cases. In some of these problems, we can use an undirected graph to represent the relation between the variables. These undirected graphs, along with a set of factors representing interaction between these random variables, are known as Markov networks. We discussed the various independencies encoded by a Markov network: local, pairwise, and global. Also, we saw that in a Markov network, the influence stops flowing as soon as we observe any node in that trail, which is quite different from the case of a Bayesian network, where different network structures imply a different flow of influence. We also discussed the concepts of I-Maps and minimal I-Maps that helped us understand when and how to encode a joint probability distribution in a graph structure. We also discussed the relationship between a Bayesian network and a Markov network.

In these first two chapters, we mainly discussed the...