Evidence Sensitivity Analysis (Decision)

Evidence sensitivity analysis (SE analysis) with respect to a decision node is the analysis of how sensitive the expected utility of a decision node is to variations in the set of observed evidence (i.e., observations on chance nodes made prior to the decision). The analysis aims to answer the questions such as, for instance, how does the expected utility of the decision change as the value observed for a single chance node is changed keeping the remaining observed nodes fixed?. The analysis is performed for each selected evidence node in turn. This can be useful for identifying the most and least important observation.

Given an influence diagram model and a decision node, the task is to computed the expected utility of the decision options for each possible value of each observed node. This is solved by iterating through the states of each observed node and computing the expected utility given that state (and the remaining set of evidence).

Using the dialog shown in Figure 1 we determine for each selected evidence variable the minimum, current, and maximum value of the expected utility of the decision.

Figure 1: The sensitivity to evidence dialog for a decision node.

Figure 1 shows the maximum expected utility (MEU) of the Drill decision given the evidence is 22.86 where the evidence is on Test (observed to yes) and Seismic (observed to open, which is an indication of some oil) in the upper left corner. For each selected evidence node, the minimum and maximum MEU are illustrated using a green bar. This shows how the MEU varies with the observed value for the selected node. The MEU as a function of the value of Seismic is between -10 and 77.5. It is -10, if we change the observed value to di (i.e., diffuse reflection pattern, which is an indication of almost no hope of oil) and 77.5, if we change the observed value to cl (i.e., closed reflection pattern, which is an indication of a lot of oil). It is clear that changes to the observed value for Seismic produce the most variation in the expected utility for the decision.