Module 4: Bayesian Networks and Influence Diagrams

Bayesian networks and influence diagrams are powerful tools for modelling and solving decision problems, particularly when the components of a problem are related in a causal manner.

Bayesian networks provide a natural tool for dealing with two problems that often occur in decision problems: uncertainty and complexity. Fundamental to the idea of Bayesian networks is the concept of modularity, whereby a complex system is built by combining simpler parts. Probability theory ensures that inferences based on a network are sound. The graphical nature of a Bayesian network makes the model intuitive for users to understand.

Influence diagrams extend the notion of Bayesian networks by including decision nodes and utility nodes. Influence diagrams provide a compact alternative to decision trees.

To illustrate the universal applicability of Bayesian networks and influence diagrams to decision problems, we cite three applications taken from finance, medicine, and anti-terrorism.

Case Study 1: Bayesian networks and influence diagrams provide a sound and transparent approach to modelling operational risks, such as settlement losses, for the financial services industry. One of the virtues of Bayesian networks in this regard is their ability to combine expert knowledge with data.
[Ref: C. Alexander (2000), Bayesian methods for measuring operational risks. ICBI Technical Risk Management Reports, ISMA Centre, Reading University]

Case Study 2: When presented with the symptoms of a patient with bacterial infection, the TREAT system uses a Bayesian network to determine the most likely cause of the infection and the antibiotic treatment most likely to be effective against the infection. The network models clinical information such as the susceptibilities of different bacteria to various antibiotics.
[Ref: S. Andreassen, L. Leibovici, M. Paul, A.D. Nielsen, A. Zalounina, L.E. Kristensen, K. Falborg, B. Kristensen, U. Frank, H.C. Schonheyder (2004). A probabilistic network for fusion of data and knowledge in clinical microbiology. In: D. Husmeier, R. Dybowski, S. Roberts. Probabilistic Modeling in Bioinformatics and Medical Informatics, Springer, London, pp. 451-472]

Case Study 3: A Bayesian network is at the heart of an anti-terrorism risk management system developed by Digital Sandbox and IET. The system is linked to a database of terrorist information. The user enters characteristics of a military base under analysis, and the system lists the most plausible threats to the base and the most significant attack points.
[Ref: L.D. Hudson, B.S. Ware, S.M. Mahoney, K.B. Laskey (2001). An application of Bayesian networks to antiterrorism risk management for military planners. Technical Report. Department of Systems Engineering and Operations Research, George Mason University]