GeNIe Tutorials: Tutorial 11 - Value of information
From DSL
Objective of the tutorial: To learn how to evaluate value of information in GeNIe.
Estimated Time: 15 Minutes
At the end of the tutorial you will be able to:
- Evaluate Value Of Information.
- Examine decisions after information is obtained.
GeNIe allows its user to compute expected value of information, i.e., the expected value of observing the state of a node before making a decision.
We will use the Bayesian network created in Tutorial 4: Creating Influence diagrams in this tutorial.
Open the Bayesian network created in the Creating Influence Diagrams tutorial.
If you do not have it saved, you can find a copy in the GeNIe/Example Networks folder. It is named tutorial4.xdsl.
You should have the following network loaded in Graph View:
Select the Value of Information option from the Network Menu as shown below:
GeNIe will display the Value of Information dialog box as shown below:
The left pane displays all the chance and deterministic nodes in the model. Since we have only 2 chance nodes, they both are displayed.
The For decision node drop list displays a list of all decision nodes in the model. Since we only have 1 decision node, " Investment Decision " is displayed in the list. This is used to select the decision that will immediately succeed the observation.
The For point of view drop list displays a list of all decision nodes in the model. Since we only have 1 decision node, " Investment Decision " is displayed in the list. This is used to select the node that is the reference point, i.e., from which point of view the value of information is being asked. This field is of importance only if there are more than one decision nodes and the decision to be made after observing the information is not the top-most decision.
The Results panel will display the results once you click on the Update button.
Since we want the value of information of the node Expert Forecast,
1. Click on the check box beside Expert Forecast in the left pane.
Since we have only one decision node, it is automatically selected from the Decision node and Point of View lists.
2. Click on Update button to calculate Value of Information [VOI].
After you click Update, GeNIe will calculate the VOI and display it in the results panel as shown below:
The forecast of our expert is worth $320 to our investor. This is the difference between the expected value of the optimal decision given perfect information about the node Forecast and the expected value of the optimal decision given no information about the node Forecast. In this case, only a 'Good' forecast benefits the investor, an expected benefit of $2000 when compared to having no information. As a 'Good' forecast will occur with frequency 0.16 the value of information is therefore calculated as $320. A positive value means that knowing the value of the node Forecast will improve the expected value of the decision. A zero value would mean that learning the value of the node Forecast before making the decision has no impact on the decision policy. It can be proven that a negative value is impossible - the intuition behind this is that we are never worse off by obtaining more information.
Let us now examine the decisions that the investor will face after she has heard the forecast. To do so, we need to add an arc between the node Expert Forecast and the node Investment Decision. After rearranging the locations of the nodes (simply left-click and drag the nodes), we obtain the following diagram:
Please note that the arc between the node Forecast and the node Invest is dashed. All arcs that enter decision nodes are informational arcs and denote the fact that the decision maker will know the outcome of the nodes at the tail of the informational arcs before she makes the decision.
Update the values using Update [ 
] button from Standard Toolbar.
After updating the values we observe the following result in the value tab of the node Invest.
Our investor should ask expert opinion (please note that the expected value of the forecast was positive) and in case the forecast is Good, she should invest in the venture. If the forecast is Moderate or Poor, however, she should not invest.
The above procedure computes the expected value of perfect information (EVPI). In order to compute the expected value of imperfect information (EVII) for a node N, you need to specify the reliability of the source of information about N by an additional node M, a direct descendant of N and then compute the EVPI for M. This will be equal to the EVII for N. This is, in fact, precisely what is being done by nodes Success and the Forecast. Node Forecast is such an imperfect source of information about node Success, characterized by the probability distribution conditional on node Success.
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