The lack of or absence of empirical data means that it is often impossible to populate all of the conditional probability tables or CPTs within a Bayesian Network using data. In such cases the only alternative is to use best guesses or expert opinion of the probabilities. A main difficulty associated with this is that CPTs can often be large, making the job of populating them with expert opinion very tedious and prone to inconsistencies.
DBL Interactive contains a built-in
CPT Calculator designed to make the job of populating large CPTs using expert opinion simpler. It works by reducing the number of scenarios (rows) in a CPT down to produce a reduced CPT. This reduced CPT contains the minimum number of scenarios required to estimate the influence that each parent node will have on the probabilities in the CPT. You then ask your expert to complete the probabilities for the reduced CPT. Once this is done, you can click on the
Calculate CPT button and the CPT Calculator will interpolate probabilities for the full CPT based on the probabilities entered into the reduced CPT. Before the CPT calculator interpolates the full CPT, it checks the logical consistency of the probabilities entered into the reduced CPT. If there are any inconsistencies, it will ask you to adjust the probabilities in the reduced CPT before proceeding.
Lets look at an example. The
Rodent Control Effectiveness Model (also listed under
Examples) contains a node called
Community TBS Effectiveness or
F, which has
five parent nodes. When this model was built, empirical data for TBS Effectiveness did not exist, so expert opinion was used to populate the CPT for the TBS Effectiveness node. This would ordinarily be a very tedious task because the CPT for the TBS Effectiveness node contains
48 scenarios. Lets look at how the CPT Calculator can make the task of populating this node simpler.
First, open the
View Networks page in DBL Interactive. Next, select the
icon beside the
Rodent Control Effectiveness Model Using CPT Calculator network. This will present you with a list of all of the nodes contained with the model. Browse to the listing for the
Community TBS Effectiveness node and click on the
Edit Probabilities link beside it. This will open the CPT for the node. Below the CPT you will see a link called
CPT Calculator. Click on this link to open the CPT Calculator (
Figure 1).
Figure 1: CPT Calculator Step 1
The first step in the CPT Calculator involves ordering the states for the node of interest (the
child node) and its parent nodes from
most positive state (
best state) to
most negative state (
worst state). In this example, the most positive state for
Community TBS Effectiveness is
High and the most negative state is
Low. There is no middle state so this is set to
N/A (
not applicable). States for the parent nodes are ordered similarly. For example, to order the states of the parent node
Farmer Participation, click on the pencil icon (
) beside it and use the drop-down menus to order the states, then click on the save icon (
). After doing this for all parent nodes (
Figure 2), click the
View Reduced Probability Table button to open up the reduced probability table (
Figure 3).
Figure 2: CPT Calculator Step 1 - ordering states
You will notice that the reduced probability table follows a particular format. The
first row in the table is the
best case scenario. That is, it is the scenario where
all parents are in the most positive state. The
last row in the table is the
worst case scenario. That is, it is the scenario where
all parents are in the most negative state.
All middle rows in the table represent scenarios where
only one parent is not in the most positive state. For example, row
two in
Figure 3 is where
TBS Lure Crops is not in the most positive state (it is
Poor) and row
three is where
TBS Maintenance is not the the most positive state (it is
Poor). Click on the pencil icon beside each row in the reduced probability table to edit the probabilities for each scenario.
Figure 3: CPT Calculator Step 2 - reduced probability table
The probabilities that you enter into the reduced probability table allow the CPT Calculator to determine the
relative influence that a state change in each parent will have on the probabilities in the CPT. It then uses this to
interpolate probabilities for all scenarios in the full CPT. Click on the
Calculate Probabilities button to run the CPT Calculator and interpolate probabilities for the full CPT of the TBS Effectiveness node. If the probabilities entered into the reduced probability table are
logically consistent then the CPT Calculator will finish and allow you to view the calculated probabilities for the node (
Figure 4). However, if the probabilities in the reduced probability table are not logically consistent then an error message will appear telling you which probabilities need to be changed.
Figure 4: CPT Calculator Calculated Probabilities
For example, in
Figure 5, the probability entered in row
two for
high TBS Effectiveness (
1) is
greater than the probability entered for the
best case scenario in row
one (
0.9). This is
logically inconsistent.
Figure 5: CPT calculator error message caused by logical inconsistency in the reduced probability table
