The first step is to generate the Q-DAG. This is accomplished by applying the Q-DAG clustering algorithm with the fault as a query variable and the sensors as evidence variables. The resulting Q-DAG has five query nodes, , , , , and . Each node evaluates to the probability of the corresponding fault under any instantiation of evidence. The probabilities constitute a differential diagnosis that tells us which fault is most probable given certain sensor values.

Figure 15 shows a stylized description of the Q-DAG restricted to two of the five query nodes, corresponding to and . The Q-DAG structure is symmetric for each fault value and sensor.

**Figure:** A partial Q-DAG for the car example, displaying two of the
five query nodes, *broken_fuel_pump* and *normal*.
The shaded regions are portions of the Q-DAG that are shared by multiple query
nodes; the values of these nodes are relevant to the value of more than one
query node.

Given that the Q-DAG is symmetric for these possible faults, for clarity of exposition we look at just the subset needed to evaluate node . Figure 16 shows a stylized version of the Q-DAG produced for this node. Following are some observations about this Q-DAG. First, there is an evidence-specific node for every instantiation of sensor variables, corresponding to all forms of sensor measurements possible. Second, all other roots of the Q-DAG are probabilities. Third, one of the five parents of the query node is for the prior on , and the other four are for the contributions of the four sensors. For example, Figure 16 highlights (in dots) that part of the Q-DAG for computing the contribution of the battery sensor.

**Figure:** A partial Q-DAG for the car example.

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