A mathematical model for modelling and calculation on the causal influence between thing. Also called causal network or influence diagram.

Basicly, a Bayesesian Network is an oriented graph where the nodes are variables (representing some phenomena, e.g. I got drunk last night or "I have a hangover") and the edges represent causal influence (e.g. if i got drunk last knight, I'm more likely to have a hangover than if i didn't get drunk).

Each variable has a finite number of states. Variables which are not influenced by other variables has an a priori probability distribution between its states. Influenced variables have argumented probabilities, so that the probability that it is in each of its states is known, if the states of the variables that has causal influence on it are known.

Bayesian Networks are used in decision support systems and troubleshooters.