Parameter Sensitivity Wizard

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.

Parameter Sensitivity Analysis

The Parameter Sensitivity panel allows us to perform sensitivity analysis on the hypothesis variable to changes on the value of the parameter variable. The sensitivity analysis is based on the sensitivity function:
f(t) = α * t + β / γ * t + δ
for computing the belief of a state of a node for a given CPT value of a parameter. The sensitivity value is computed based on the function
f(t)= α* t + β / (γ * t + δ)2

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 CPY 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.

Import a case file

It is possible to perform parameter sensitivity analysis on a case stored in a case file or a set of cases stored in a data file. A case file represents a single case whereas a data files represents a number of cases for a given network.

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-cases1"  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. Sensitivity analysis can not be performed on a hypothesis node with evidence entered.

Figure 2: Sensitivity analysis with evidence from a case file.

Open Network

The "Sensitivity Set Graph Panel" is a tool to help visually capture the results of the parameter sensitivity analysis, directly on the network. It is accessibly by pressing the "Open Network" button in the "Parameter Sensitivity Panel".

Every node is divided in three and every division 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 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 "Has Lung Cancer" 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".