## What Is A Bayesian Belief Network?

Today’s post on the IDI Blog is an introduction to topic that is rapidly gaining traction in the analytical community: Bayesian Belief Networks.

A Bayesian Belief Network (BBN) is a way to represent a probability model. In such a network, variables appear as nodes and arcs between the nodes represent probabilistic dependence between variables. Conditional probabilities encode the strength of the dependencies. For example, a BBN could be used to represent a medical test, where the result of the test indicates the likelihood a disease is present.

A BBN also provides a way to perform calculations on probability models. They can be used to compute the probabilities for hypotheses nodes given evidence entered into other nodes, for example nodes representing symptoms. They can also be used to compute other measures, such as the diagnostic strength of a piece of evidence. In the example above, suppose a disease is present in 1% of the population at any time. When present, the disease is known to generate a positive test result 99% of the time, but a false positive occurs 5% of the time when the disease is absent. Lacking other evidence (symptoms), a BBN could be used to calculate that a positive test raises to 17% the likelihood the patient actually has the disease.

This is a very simple example for which we don’t really require a BBN. For one thing, the graph of the BBN is a tree – there is a unique path between all nodes. BBNs gain their power in capturing multiple co-dependencies, where the tree structure can be violated.

Here’s a visual example of a BBN that represents a generic attacker-defender risk model. This is a picture taken of a Netica representation, where we see the nodes, but don’t see the states or underlying numbers. Netica is one of many software packages on the market that handle BBNs.

Examples of areas Bayesian Belief Networks have been applied:

- Assessing status of adversary uranium enrichment programs
- Understanding and predicting adversary decisions and intent
- Diagnosing liver disorders for clinical practice and training
- Validating human intelligence assets and credibility of evidence
- Assessing tax audit risk
- Analyzing risk in the development of a major software system
- Tracking groups of pedestrians in video sequences
- Visual tracking of dynamic targets in complex environments
- Determining functions of WMD-related facilities
- Assessing critical situations for a nuclear power plant

To learn more see:

A page that is no longer maintained but with excellent material: __http://www.eecs.qmul.ac.uk/~norman/BBNs/BBNs.htm__

A nice intro from Microsoft:

A link to Norsys, the company that makes Netica: __http://www.norsys.com/belief.html__