Tricks Of The Trade - Bayesian Belief Networks

Bayesian belief networks offer a powerful new tool with which to analyse and quantify op risk, says researcher

Brendon Young.

Op risk practitioners at banks are currently showing great interest in the use of Bayesian Belief Networks (BBNs).

The approach has yet to be tested in the financial industry, but it seems to offer a straightforward and intuitive method of quantifying op risk.

Indeed, practitioners who are learning about the technique say that it seems to formalise in a useful way many of the analyses that they already undertake.

One reason BBNs are attractive is their flexibility. They can be applied to firm-wide or "top down" approaches to op risk, as well as to more detailed "bottom up" approaches.

They offer a way of incorporating both objective data and subjective judgements. And they can be applied even where data are incomplete.

Unlike other methods such as extreme value theory, BBNs allow both forward and backward inference.

They can help practitioners quantify risks that have already been noted in op risk and audit checklists. They also help to make any assumptions about the impact of risks more transparent, and so provide an auditable record.

Where does the approach come from?

The mathematical theory that underpins the BBN approach was developed by the Rev. Thomas Bayes around 200 years ago.

However, the approach could only be put to limited practical use until recent breakthroughs in the development of efficient propagation algorithms (Lauritzen and Spiegelhalter 1989; Pearl 1992).

Tools incorporating these algorithms have now been developed (e.g. www.hugin.dk). These allow analysts to create very large and complex models.

To date, one of the largest models constructed is a decision-support system for improved predictions of the reliability of prototype military vehicles. This model, developed for the Ministry of Defence in the United Kingdom, made use of several million nodes (TRACS, 1999).

Over the last few years BBNs have been applied to all sorts of problems that demand very high levels of reliability and safety such as:

 Determination of the reliability of software.

 Medical diagnosis.

 Establishment of the probability of innocence/guilt of a defendant in a court trial.

 Diagnosis of space shuttle propulsion systems (VISTA by NASA/Rockwell)

 Situational assessment of a nuclear power plant

Less inspiringly, BBNs form the basis of Microsoft’s Office Assistant (Heckerman et al., 1995).

How do BBNs relate to traditional decision trees?

Figure 1 illustrates the traditional approach to decision analysis. This simple example shows two probabilities, p and q, with respective values of 0.7 and 0.8.

The probability of both these events occurring is simply a function of these two values (ie, 0.56). Note that all the possibilities (ie, the sum of all the probabilities) total to unity.

This kind of simple decision tree is useful for modelling chains of causal events, where the events unfold in a single direction.

However, a decision tree cannot handle, among other things, the backward propagation of evidence. That is, it cannot help analysts to link a consequence back to its underlying cause.

And the traditional decision tree does not allow for the specification of common causes, ie multiple consequences arising from the same (parental) causal events.

How do BBNs improve on decision trees?

The essence of Bayesian probability theory is that it offers a technique for re-assessing probabilities in the light of additional information.

The tool it uses to do this is the BBN. A BBN is a directed graphical representation model consisting of nodes that represent variables, and arrows (arcs) that represent probabilistic dependencies between variables.

A simple BBN graph is given in Figure 2. As can be seen, in this example the full BBN is made up of four sub-graphs.

For clarity, we have not added the mathematical apparatus to the Figure, but in practice each of the nodes would contain the state of the variable that it represents and a conditional probability table (CPT).

Putting BBNs into practice

The two major problems for risk practitioners setting out to build a BBN are:

1. Determining the activity/event nodes and the relationship between the nodes.

2. Obtaining the probabilities/estimates for each node.

Two major advances have greatly simplified the creation of complex networks.

First, standard modules of frequently occurring nodes and arcs (idioms) have been identified (www.agena.co.uk). This means that most BBNs in the field of safety and reliability can now be substantially constructed from combinations of a handful of idioms.

Second, it is no longer necessary to identify all of the probabilities/estimates in a network. In practice, it is only necessary to determine probabilities/estimates at the "boundaries" of the network.

The remaining values can then be extrapolated automatically using an elicitation process.

BBNs and financial institution op risk

While the use of BBNs is relatively advanced in industries such as computer and software engineering, it is in its infancy in the financial services sector.

Practitioners who have looked at the technique say BBNs may be appropriate for such tasks as:

- Supporting capital computation and allocation.

- Monitoring against key performance measures.

- Validating self-assessment reviews through the provision of independently justified results.

However, a number of issues arise out of the relative complexity of bank systems.

In order to predict loss by product and by customer with sufficient accuracy, it may be necessary to create a number of sub-networks rather than a single network that attempts to bring together all products and customers.

Another issue is the need for correlation analysis in operational risk measurement. That is, the problem of working out whether some risks rise and fall in tandem, and how much these risk correlations affect a portfolio of op risks at a financial institution.

For most organisations, a detailed correlation review of the institution’s portfolio of op risks would prove prohibitively difficult and expensive. Many variables in the operational environment are non-numerical, and therefore not readily analysed in terms of correlation. This problem is currently the subject of debate among op risk practitioners.

An alternative may be contingency analysis, since the tables created through the analysis represent estimates of a conditional probability table.

It can be argued that, by definition, the output of BBN modelling indicates the level of correlation between each of the variables that lie within the network.

Changing nodes and linkages using a BBN-based software program offers a fast way of testing the strength of any dependency -- whether the nodal linkage is subjectively or objectively identified.

It follows that using the BBN approach might obviate some of the need for correlation analysis.

How to apply BBNs

There are four stages in the application of BBNs:

1. Initial familiarity with the technique. This can be obtained by exploring the web sites and texts listed below.

2. Construction of a simple top-down network. This could be developed by Group Operational Risk at a bank and should initially consist of a relatively few nodes and arcs. The network can later be expanded as appropriate, but it should not be made too detailed.

3. Development of separate bottom-up BBNs for each business unit

. This should be carried-out by the business units themselves and should be related to quantification efforts that make use of existing checklists.

4. Linking the various separate networks. It may be considered appropriate at a later stage to link the bottom-up business unit network modules to the top-down group network to form a holistic, enterprise-wide knowledge management system. However, complexity can lead to chaos!

Quantification represents the next major step forward in op risk. However, firms need to approach it with an air of caution. It is not possible to quantify everything, even if all risks could be identified -- which they cannot.

There are many mathematical tools and techniques available, all with their particular applications. BBNs are a particularly powerful addition because they not only help in the quantification effort, but also facilitate knowledge management in a much wider sense.

Brendon Young is Director of the Centre for Operational Risk Research & Education and Chairman of the UK’s Operational Risk Research Forum. He is former director at associate dean level of UCE Business School.

Email: [e-mail]

Information sources

Web sites:

www.agena.co.uk; www.hugin.dk

Jensen, F.V., 1996

An introduction to Bayesian networks

UCL Press

Lauritzen, S.L. and Speigelhalter, D.J., 1988

Local computations with probabilities on graphical structures and their application to expert systems [with discussion]

J. R. Stat. Soc. B, 50, no 2., pp. 157-224

Pearl, J., 1988

Probabilistic reasoning in intelligent systems

Morgan Kaufman, Palo Alto, CA.

TRACS (Transport Reliability Assessment & Calculation System): Overview, 1999

DERA project, E20262, http://www.agena.co.uk/tracs/index.html

Fenton, N.E., et al., 1998

Assessing dependability of safety critical systems using diverse evidence,

IEE Proceedings Software Engineering, 145(1), 35-39.