Let's start with a refresher course in basic statistics.

Given two events or observations, X and Y, the joint probability of X and Y is defined as . If the observations X and Y are not related, an assumption known as conditional independence, then p(X,Y) = p(X).p(Y). The conditional probability of event Y, given X, is defined as p(Y|X)=p(X,Y)/p(X).

These two definitions are quite simple. However, probabilistic reasoning can be difficult to read in the case of large numbers of variables and sequences of conditional probabilities. As a picture is worth a thousand words, researchers introduced graphical models to describe a probabilistic relation between random variables [5:1].

There are two categories of graphs, and therefore, graphical models:

Directed graphical models are directed...