A Decision Node and one more Utility Node
Now, you are about to add the decision node Treat (see figure 1). This is done similar to the way you add chance nodes and utility nodes:

• Press the decision tool (to the right of the utility tool)
• Click somewhere in the network pane (a good place would be to the right of the Dry node)
• Change the name and label of the new decision node to "Treat"

You add an action to a decision node in the same way as you add a state to a chance node:

• Choose the Treat node as the currently active node by selecting it from the drop down list below the tool bar or simply by double clicking it
• Press the add state tool
• Change the action names to "treat" and "not"

The Treat decision node has an impact on the Sick' node so:

• Add an arrow from Treat to Sick'

The new decision node represents the decision to give the tree some treatment or not. If the plantation owner (Apple Jack) chooses to give treatment this will cost him something which shall be modeled by the Cost utility node. The Cost node has the utility table shown in table 2.

Now, add the Cost utility node to the influence diagram:

• Add a new utility node (a good place would be to the right of the Treat node)
• Change the name and label of this node to "Cost"
• Add an arrow from Treat to Cost
• Fill in table 2 in the utility table of Cost

Filling in CPTs
When we copied the nodes Sick' and Dry', they inherited the CPTs of Sick and Dry. However, as both these nodes have become children of other nodes, their CPTs are no longer correct. Their new CPTs were specified to those found in table 3 and table 4.

• Fill in table 3 as the cpt of Sick'
• Fill in table 4 as the cpt of Dry'

Now, your influence diagram is finished and it should look like the one in figure 4. At this point it would be a good idea to save your influence diagram.

Figure 4: The complete influence diagram

Compiling the influence diagram
You can now try out the influence diagram and hopefully you are eager to see how it works. First, compile the influence diagram:

• Press the compile tool (the right most tool button in the network window tool bar)

In addition to the errors described in the first tutorial in the case of influence diagrams the compiler also checks that there is a directed path through all of the decision nodes - if not it will return an error message. If the influence diagram does not compile, you have probably made some minor error. You should first check that the causal arrows are correct. Then, go through each of the CPTs/utility tables of the nodes.

What Should Apple Jack Do ?
When the influence diagram has been compiled, first imagine that the only thing Jack knows about his tree is that it is losing leaves. Then, what will be the best thing for him to do? To find out this, follow these steps:

• Expand the Loses chance node and the Treat decision node in the node list pane on the left (by double clicking them)
• Enter the evidence that Loses is "yes" (by double clicking the "yes" state)
• Propagate the influence diagram (press the sum propagation tool)
• Read the expected utility of "treat" and "not" in the Treat decision node

You should be reading something looking like that in figure 5.

Figure 5: The influence diagram propagated with the evidence that Loses="yes".

You read 10234.4 as the expected utility of giving treatment and 11514.0 as the expected utility of not doing anything. This suggests that it will be best for Apple Jack not to treat the tree.

If you read other values than those specified above, you have probably mistyped something when filling in the CPTs. Then, check the CPTs/utility tables of all the nodes.

In a decision situation, your opinion about what to do will sometimes change when you learn more facts about your situation. Lets see what happens if Jack knows that it has been raining a lot lately and that the tree under no circumstances can be suffering from drought. Then the state of Dry can be set to "not":

• Enter the evidence that Dry is "not"
• Propagate the influence diagram
• Read the expected utility of "treat" and "not" in the Treat decision node

You should read 9138.33 as the expected utility of giving treatment and 5918.33 as the expected utility of not doing anything. In this case, it will obviously be best for Jack to give the tree some treatment.

The reason for the difference between these two cases is that in the first case, it is likely that the tree is suffering from drought. Then, of course, the costs of treating the tree for a sickness will not pay off.

This finishes the tutorial. You should now be able use the Hugin GUI to construct your own influence diagrams. However, if you want to create large and complex models, we suggest that you study the area more.