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The Mildew Examples
By: Finn V. Jensen
The Mildew examples are four different influence diagrams modeling the situation where a farmer has to decide on a treatment with fungicides for a wheat field. The influence diagrams model different scenarios depending on the information available.
The basic situation
These examples originates from the book "An introduction to Bayesian Networks" .
Approximately two months before harvesting a wheat field a farmer can observe the state of the crop and he can observe whether it has been attacked by mildew. If there is an attack he should decide on a treatment with fungicides.
The influence diagram below models this situation:
There are five chance nodes:
- The actual state of the crop, Q with states fair (f), average (a), good (g) and very good (v)
- The actual mildew-situation, M with states no, little (l), moderate (m) and severe (s)
- The state of the crop at harvest time, H with the states from Q plus rotten (r), bad (b) and poor (p)
- The observation, OQ, of Q
- The observation, OM, of M
There is also an action node, A (modeling the fungicide-treatment) with actions no, light (l), moderate (m) and heavy (h).
As the influence diagram has only one decision node you can enter evidence into any chance node and the Hugin GUI will calculate the expected utility of the decision options.
This network has been installed on your computer with the Hugin software. You can find the network in the Samples subdirectory of your hugin installation.
Now we extend the example with a decision on the time of harvest (T). This decision is to be made two months after the decision on fungicides. Note that H models the state of the field at the time of decision T.
When there are more than one decision node in the model, the calculation of the expected utility of an action requires knowledge of what will be known when future decisions are made. Also, information links into decision nodes must be provided. A link from node X to decision node D indicates that the state of X is known when the decision on D is made.
The temporal order of decision variables is established by ensuring that there is a directed path connecting all decision nodes. The Hugin GUI assumes "no forgetting", which means that if there is a link from X to D, you need not have a link from X to the successors of D.
The model depends on what information is available at the time of deciding on T. We present three different scenarios:
Scenario 1
In this scenario there is no further information.
If you enter the state of OQ and the state of OM, the Hugin GUI will calculate the expected utilities of the states of A under the assumption that T will be decided optimally.
This network has been installed on your computer with the Hugin software. You can find the network in the Samples subdirectory of your Hugin installation.
Scenario 2
In this scenario the state of H is known. This means that there is a link from H to T. A link from a chance node to a decision node means that evidence on the chance node has to be available at the time of the decision in order for the utilities to be calculated correctly.
This network has been installed on your computer with the Hugin software. You can find the network in the Samples subdirectory of your Hugin installation.
Scenario 3
In this scenario there is an observation on H available, but it is imprecise, so it doesn't necessarily show the actual state of the crop. Still it has an impact on our belief in the state of H and also on the expected utilities of the various possibilities for T.
This network has been installed on your computer with the Hugin software. You can find the network in the Samples subdirectory of your Hugin installation.