Belief Networks to Support Decisions
Food safety - a complex scenario ...
At IFR we are developing new information handling techniques and sophisticated communication tools to help people to appreciate and understand the complex situations that are involved with food safety on the farm, at the factory, in the supermarket and at home in the kitchen.
Decisions, Decisions ...
Making a decision about food safety is often very difficult ... especially if there are many variables to consider or if the information available is incomplete and uncertain.
Computer tools called belief networks can be programmed to help with decision-making and, therefore, can help to explain choices and strategies in unclear situations.
Models of Beliefs ...
We can illustrate belief modelling and an automated decision making process with a very simple example ...
- A closed box contains ten tokens. Although we know that each token can be either black or white we do not know the actual colours of the tokens. We know white tokens are ‘best’ so … we would like to be sure that all the tokens in the box are white.
- We could test the tokens – to do this we take a token from the box, examine it to see whether it is white or black, and return it to the box. Obviously we could repeat this test several times to get better information about the colours. If we keep testing and the answer is always white we would be increasingly confident about the ‘quality’ of the tokens in the box even though there is a small chance that we keep taking the same token from the box!
This complex situation can be represented by a flow diagram.
The arrows in the diagram tell us that the result of our testing (whether all the tokens we pull out are white or not) depends on the number of black tokens in the box and on the number of times we take out a token and look at it.
In fact this is far more than a flow diagram because it has been programmed to compute a belief … the belief concerning the number of black tokens in the box based on the result of a test.
If you click on the picture (below), a new window will appear on your screen. The window will be running an IFR Servlet that will enable you to interact with the belief network (above).
You can use the buttons to prime the network with a ‘test result’ and then a bar chart indicates what you should believe about the number of black tokens in the box based on the test … No test can be categorical so the computed belief is still a probability but the probability falls on the side of the test results.
| Example 1 |
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Should we Shouldn't we?
This situation is easily extended … Imagine that it costs £100 to manufacture a box of ten tokens and that each token tested adds £1 to this expense … On the plus side we could earn £200 from the sale of a box containing ten white tokens and on the debit side there is an unknown penalty for selling a box that includes any black tokens …
Should we sell?
The new belief network has an additional uncertain variable to represent the size of the penalty and some diamond shaped nodes that represent the contributions to the bottom line …
This network still computes the underlying probabilities … but, based on these, it also expresses what we can expect to gain or lose by selling the box of tokens … we could base a decision to sell the box on this expectation.
As in the previous example, if you click on the picture (below), a new window will appear on your screen. The window will be running an IFR Servlet that will enable you to interact with the belief network (above).
In the network (below) you can examine the expected return for different scenarios involving observed test results and belief concerning the penalty factor … In general small penalties and large negative tests favour sale … If we believe the penalty to be very large it is often favourable to refrain from the sale and accept the smaller of two losses 
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| Example 2 |
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Deciding what to do …
We may use the new representation of information to develop a strategy …
How many tests give us an optimal return?
As in the previous example, if you click on the next picture (below), a new window will appear on your screen. The window will be running an IFR Servlet that will enable you to interact with the extended belief network.
If we have a firm knowledge of the penalty we can easily find an optimum strategy for testing. The frame below can be used to show that when the penalty (for selling black tokens) is £10 we can maximise the expected return from a sale by taking 10 samples … just enter the five sample sizes in turn and follow the variation of the expected return
| Example 3 |
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Whose Decision is it anyway …?
A set of options often reflects the priorities of the person who intends to make a decision … but the network representation of information is not so blind 
. It is straightforward to use the tool above to answer complementary questions e.g. “What level of penalty should be imposed to encourage an adequate degree of testing?” … Other quality indicators can be assessed in parallel too … It’s not who decides its what is known that matters.
More than token problems …
Real world problems are more complex than the one above but the same elements are usually involved … uncertain information, dependent events and multiple viewpoints. It is not a big step to turn the ‘tokens in a box’ scenario into a realistic model for control of food contamination and quality assurance.
| Examples of real-life sampling problems |
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At the Institute of Food Research food safety experts, mathematical modellers and webmasters come together to represent real food safety issues as accessible, interactive, tools that support consistent debates and specific queries.
Additionally, IFR has other research groups tackling the psychological aspects of food risks e.g. people's perceptions
The problem with complexity …
The interactive controls on this page compute the answer for every query in real time … they don't read an answer from a list of all the possible answers! This is crucial … although it is possible to make a full list of answers for hypothetical problems like ‘tokens in a box’ the list would be too long … (in fact, becoming exponentially long …) for any real food safety scenario.
At IFR we believe that list-based (even hyper-list based) representations of safety information will soon be replaced by dynamic tools that allow emergent views and individualised interrogations … a way to cope with life’s complexities.
Sharing …
The belief computations take place on a server at IFR and can be delivered to most flavours of browser. Modern technology allows the calculations to find and use data from widespread sites so that there may be many contributors to each real assessment … its easy to envisage a global data environment for future food safety assessments akin to the environment in which modern molecular biology is performed today.
At IFR we are constantly adding new information on food safety issues, we are researching improved computational methods to make the most from uncertain data and we are building web delivery systems to make food safety issues accessible to a wide audience.
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Last update 05/11/2009
