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Figure 1: A LIMID modeling the oil wildcatters decision problem. |
In this example, an oil wildcatter must decide either to drill or not to drill. He is uncertain whether the hole is dry, wet or soaking in oil. The wildcatter can make seismic soundings that will help determine the geological structure of the site. The soundings will give a closed reflection pattern (indication for much oil), an open pattern (indication for some oil) or a diffuse pattern (almost no hope for oil).
The wildcatter has two decisions to make, namely whether to test with seismic soundings costing K$10 and whether to drill costing K$70. The utility gained from drilling is determined by the state of the hole (dry, wet or soaking).
The domain of this problem is modeled by the (limited-memory) influence diagram (LIMID) in Figure 1. Note the link from Seismic to Drill. It specifies that when the decision of Drill has to be made, the state of Seismic is known. If this link is not specified, the computations will be made under the assumption that this observation is not known by the decision maker when she has to make the drill decision.
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Figure 1: A LIMID modeling the oil wildcatters decision problem. |
In Figure 1, the chance node Oil has states "dry", "wet", and "soak", the chance node Seismic has states "closed", "open", and "diff", the decision node Test has actions "test" and "not", and the decision node Drill has actions "drill" and "not". In Tables 1 and 2, the CPTs of the nodes Oil and Seismic are shown. In Table 3 and 4, the utility tables of the utility nodes Pay and Cost are shown.
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| Table 1: P(Oil). |
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Table 2: P(Seismic | Oil, Test). |
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| Table 3: U(Pay). | ||||||||||||||||||
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| Table 4: U(Test). |
The LIMID is now constructed using the Hugin Graphical User Interface and after compilation and a Single Policy Update, the results can be seen in the initial state of Figure 2. The only important values to read at this point are those of Test. Hugin has no way of knowing whether the wildcatter chooses to test or not. Thus, the values of the nodes depending on Test will not be correct.
| Figure 2: The results of solving the LIMID. You can click the states of Seismic to read the expected utility of drilling given the result of the seismic soundings. Initially, the Figure shows the result of a propagation before anything is known about whether the wildcatter will test with seismic soundings or not. At this point, the values of the other nodes cannot be computed correctly and should be ignored. |
We see that the expected utility of testing is K$22.5 while the expected utility of not testing is less. This implies that it will be best for the wildcatter to test with seismic soundings which will give him the states of Seismic. If you try to click at the state names of Seismic in the Figure, you can see what happens to the expected utility of Drill when the seismic test has come up with a result. If you choose "closed", the expected utility of drilling is K$77.5. Else, if you choose "open", the expected utility is K$22.9 and if you choose "diff", the expected utility is K$-40.5. In the last case, it will obviously be better not to drill only giving expected utility K$-10.0.
This network has been installed on your computer with the Hugin software. Open the network in the Hugin Graphical User Interface (Note: not all browsers can open Hugin directly). You can find the network in the directory where you installed Hugin (e.g. C:\Program Files\Hugin\Hugin Lite\Samples).You can also find the samples at the Hugin download area.
