## Bayesian Belief Network (Bbn)

A Bayesian belief network (Bbn) is a set of nodes representing random variables and a set of arrows connecting these nodes in an acyclic manner. Each node has assigned a function which describes how the state of the node depends on the parents of the node.

In Hugin Bbns, you can represent two kinds of random variables: discrete chance nodes having a discrete finite state space and continuous chance nodes having a continuous infinite state space.

For the discrete chance nodes, the function describing how the node depends on its parents is a conditional probability table. For continuous chance nodes it is a pdf (in Hugin it must be a Gaussian normal distribution function).

In Hugin, you can also compose influence diagrams which are Bbns extended with decisions and a utility function.

A Bayesian belief network (Bbn) is really just a smart representation of a domain of dependent random variables.

Many real life situations can be modelled as a domain of random variables (you could model a group of related deceases: risk factors, deceases, and symptoms). A domain of random variables could form the basis of a decision support system to help actors decide what would be most beneficial in a given situation.

If you wanted to represent a domain of random variables (all having a discrete and finite state space), you could always do this by the joint probability table of the entire domain. That is, a table with an entry for each configuration of the nodes of the domain. However, the number of configurations of a domain grows exponentially in the number of random variables so this would only work for very small domains.

What you use to keep the representation size to a minimum in Bbns is the conditional independencies in the domain: Very often the knowledge about a random variable being in a specific state will make other variables independent and thus it would be overkill to have an entry for all combinations of these independent variables (they would all contain the same value).

This is not the right place to describe the theory behind Bbns in detail. You should be able to find some useful literature about the subject elsewhere. Here is a place to start: Finn V. Jensen: "An Introduction to Bayesian Networks" - May 1996.

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