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

Bayesian networks support variables that have more than two possible values. Koller and Friedman's "Probabilistic Graphical Models" has examples with larger variable domains.

Usually BNs have discrete random variables (with a finite number of different values). But it's also possible to define them with either countably infinite, or continuous variables. In the latter case, the inference algorithms change considerably, though.

Now that I tried finding some examples online, I have to admit you're correct. They're hard to find. Here is an example that is taken from above book. The variable Grade can take on three different values.