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.