Preliminaries

Distributions

Suppose variable $A$ has 2, $B$ has 2, and $C$ has 3 possible values. Their joint probability distribution will contain $2 \times 2 \times 3 = 12$ values.

We can condition the distribution by setting a variable to a specific value.

We can also marginalize the distribution over a subset of variables to examine the distribution of a single variable.

Factors

A factor $\phi$ is a function that maps values of variables (e.g., $A$, $B$, and $C$) to a real number.

The set of variables that the factor takes as arguments is called the scope of the factor.

Both normalized and unnormalized measures are examples of factors, although their scopes may vary.

A Conditional Probability Distribution (CPD) is another common example of a factor.