in probability, a factor \(\phi\) is a value you can assign to each distinct value in a discrete distribution which acts as the probability of that value occurring. They are considered parameters of the discrete distribution.

If you don’t have discrete variables, factors allow you to state \(p(x|y)\) in terms of a function \(\phi(x,y)\).

See also Rejection Sampling

## factor operations

### factor product

\begin{equation} \phi_{3} (x,y,z) = \phi_{1} (x,y) \cdot \phi_{2}(y,z) \end{equation}

### factor marginalization

\begin{equation} \phi(x) = \sum_{y=Y} \phi(x,y) \end{equation}

### factor conditioning

Removing any rows not consistent with evidence. Say you know \(Y=1\), remove all rows that say \(Y=0\).