Bayes Networks

A Bayes Network is a finite directed acyclic graph (DAG) with vertices representing variables $X_1,\dots ,X_n$, and a conditional probability table $p(X|\pi (X))$ for each vertex. These tables define a joint probability distribution on the Boolean random variables $X_1,\dots ,X_n$ given by the equation

$$p(X_1,\dots ,X_n)=\prod _{i=1}^{n}p(X_i\mid \pi (X_i))$$

Note

The set of parents $\{x_0,\dots ,x_n\}$ of a node $\alpha$ is given by $\pi (\alpha )$.

Each variable $X_n$ is related to a proposition letter $x_n$ and can take the value either $x_n$ or $\neg x_n$.