Do variables in Bayesian Networks have to be Boolean?

Question

I can't believe I can't find any information on this, but do variables in Bayesian Networks have to be boolean? Every example I've found in my textbook or online uses T/F variables, but how do I represent a variable that has more than two possible values in a Bayesian network?

For example, I was given the following problem:

We have a bag of three biased coins a, b, and c with probabilities of coming up heads of 20%, 60%, and 80%, respectively. One coin is drawn randomly from the bag (with equal likelihood of drawing each of the three coins), and then the coin is flipped three times to generate the outcomes X1, X2, and X3.

Draw the Bayesian network corresponding to this setup and define the necessary CPTs (Conditional Probability Table).

Can anyone help point me in a direction to get started with this?

Answer 1

The Bayesian network is nothing more than a graphical way of representing a set of conditional independence assumptions. Say, for instance, if X and Z are independent variables(under some conditions) given Y, then you could draw the Bayesian network X → Y → Z. And conversely, the only thing that the Bayes net X → Y → Z tells you is that there are three variables (X, Y, Z) and that X and Z are conditionally independent given Y.

Once you understand this, then you realize that anything you could write a conditional independence assumption for, you can draw a Bayes net for, and vice-versa.

That means, they need not be Boolean at all.