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.
|
Treat="treat" |
Treat="not" |
| -8000 |
0 |
|
| Table 2:
U(Cost). |
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'
|
Treat="treat" |
Treat="not" |
|
Sick="sick" |
Sick="not" |
Sick="sick" |
Sick="not" |
|
Sick'="sick" |
0.20 |
0.01 |
0.99 |
0.02 |
|
Sick'="not" |
0.80 |
0.99 |
0.01 |
0.98 |
|
| Table 3:
P(Sick' | Sick, Treat). |
|
Dry="dry" |
Dry="not" |
|
Dry'="dry" |
0.60 |
0.05 |
|
Dry'="not" |
0.40 |
0.95 |
|
| Table 4:
P(Dry' | Dry). |
Now, your
(limited memory) influence diagram (LIMID) is finished and it
should look like the one in figure 4. At this point it would be a
good idea to save your LIMID.
|
|
Figure 4: The complete influence diagram |
Compiling the Limited Memory Influence
Diagram
You can now try out the LIMID and hopefully
you are eager to see how it works. First, compile the LIMID:
- Press the compile tool (the right
most tool button in the network window tool bar)
The compilation of an influence diagram
may produce some of the same errors as described in the
first tutorial. If the LIMID
does not compile, you have probably made some minor error. Once
the influence diagram has been compiled, probabilities and
expected utilities are computed under the initial policy. To
solve the influence diagram it is necessary to invoke Single
Policy Updating.
What Should Apple Jack Do ?
When the LIMID has been compiled, you should
do a Single Policy Updating. Now, 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
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.
This finishes the tutorial. You should now be
able use the Hugin Graphical User Interface to construct your own
(limited-memory) influence diagrams. However, if you want to
create large and complex models, you should study the area more
than just reading this tutorial.
