Let
, be a set of variables.
A *Bayesian network* over a set of variables is a *network structure* , which is a directed acyclic graph (DAG)
over and a set of probability tables
where is the set of parents of in . A Bayesian
network represents a probability distributions
.

Below, a Bayesian network is shown for the variables in the iris data set.
Note that the links between the nodes class, petallength and petalwidth
do not form a *directed* cycle, so the graph is a proper DAG.

This picture just shows the network structure of the Bayes net, but for each of the nodes a probability distribution for the node given its parents are specified as well. For example, in the Bayes net above there is a conditional distribution for petallength given the value of class. Since class has no parents, there is an unconditional distribution for sepalwidth.

Remco Bouckaert 2008-05-12