 |
| Figure 1: Parameter Sensitivity Analysis |
Parameter Sensitivity analysis is the analysis of how sensitive the results of a belief update (propagation of evidence) is to variations of the value of a parameter of the model. The parameters of a model are the entries of the conditional probability distributions.
In the following example (Figure 1.) the asia.net network is loaded and compiled before entering the Parameter Sensitivity Panel (available from the "Wizards" menu in Run-mode). The "Has bronchitis" node is selected as the hypothesis variable and "All States" is checked so an analysis will be performed on all states of the Hypothesis node. The node "Smoker" is selected as the parameter variable. When selecting a parameter variable it's CPT table is displayed at the bottom of the panel (Figure 1).
| |
| Figure 1: Parameter Sensitivity Analysis |
By clicking on yes = 0.5 in the CPT table, the sensitivity function is used to compute a value (belief) for each state of the hypothesis variable. A graph is displayed on the top right corner of the panel, showing two lines that represent how sensitive the states of the hypothesis variable are, to changes to in the parameter values, i.e., the entry of the CPT selected which in the example is yes = 0.5.
From this graph we notice that the state of the hypothesis variable with highest probability changes when the parameter value is above approximately 0.7. Also, notice that the sensitivity function is a straight line. Given that "Smoker = yes = 0.5" the belief that the patient has bronchitis is 0.45 and the belief that he doesn't have bronchitis is 0.55. These points (0.5, 0.45) and (0.5, 0.55) are shown on the graph.
Sensitivity analysis can not be performed for extreme CPT values,
i.e., zero and one.
When the hypothesis node has many states, the graph can become
confusing because of overlapping sensitivity function lines. By
selecting a state in the graph information table (upper - left), only
the sensitivity function line for the selected state will be displayed
in the graph. To see all lines again, select a CPT index in the
Parameter variable table.
The table located in the middle of the panel (Figures 1a, 1b), is
the CPT table of the node selected in the Parameter Variable combo.
When selecting a cell in the table, sensitivity analysis is performed
using the selected cpt value. The radio boxes "MIN SV" and "MAX SV"
allows the user to view a color chart that represents the sensitivity
values for every cpt index. The intensity of the red or blue colors
inticate the size of the sensitivity value.
Figure 1a: CPT table of Dyspnoea with a color chart showing the minimum Sensitivity values.
When a cholor chart with the minimum sensitivity values is selected, the darker the red color is, the lower the sensitivity value is for the coresponding cpt value (Figure 1a).
The "Case File" button imports a file in the wizard and gives the user the posibility to select cases and enter them as evidence in the domain. Sensitivity analysis can now be perfomed for each case in the file. In Figure 2, a case file "asia-cases" is imported and displayed as a table. When clicking on a case, it is entered as evidence in the domain and after performing sensitivity analysis as shown above (Figure 1), the sensitivity values calculated and the lines in the graph, are different because the new evidence is taken in to consideretion.
 |
| Figure 2:
Sensitivity analysis with evidence from a case file. |
Every node is divided in three parts and every part is painted in a different colour. Starting from the left of a node, the colours used are blue, red and green which represent different values.
The blue colour (left) represents the maximum sensitivity value.
The red colour (center) represents the minimum (negative) sensitivity value.
The green colour (right) represents the average sensitivity value.
The tone of each colour, indicates how high the value they represent is. In case of the maximum and average sensitivity values(blue, green), the higher the number is, the darker the colour becomes. In case of the minumum (red) value the opposite applies. If a value is 0, the colour gets toned down to white. The yellow colour indicates that it was not possible to compute sensitivity values for that node, either because evidence is enterered in the hypothesis node or because the values in the node's CPT table are 0 and 1.
 |
| Figure 3: Sensitivity set graph |
Figure 3 shows an example of the "asia" network. In this example,
it is immediately visible which nodes have the highest values and which
have
values 0 or close to 0. By pointing on the "Dyspnoea" node, the
node's minimum, maximum and average values are displayed at the bottom
of the
panel together with it,s name and label. Selecting a node on the
network will
set it as the parameter variable in the "Parameter
Sensitivity Panel".