Optimizing Model Parameters

We performed a set of experiments in which we considered the BARD simulation model as a gold standard, and then optimized the PANDA detection model based on the BARD model. Optimizing the PANDA model required a change to both the structure of the person Bayesian network and to its parameters. The structure of the optimized person model is shown in Figure 18.6.

figure 18.5 An AMOC curve showing the detection capabilities of PANDA over different anthrax concentrations.
figure 18.6 The optimized person model.

One of the main differences between the optimized model and the original model is the removal of the previously existing arc from the Anthrax Infection node to the Respiratory from Anthrax node. We also add an arc from the ED Admit from Anthrax node to the Respiratory from Anthrax node. These changes are intended to reflect the behavior of the BARD simulator, which assumes that all patients infected with respiratory anthrax will exhibit respiratory symptoms. Therefore, all patients who are admitted to the ED due to a respiratory anthrax infection are assumed to exhibit respiratory symptoms.

We estimated the optimal parameters for the Anthrax Infection node and the ED Admit from Anthrax node over a training set obtained from the BARD simulator that was separate from the test set used to evaluate the performance of the PANDA algorithm. The training set consisted of 96 anthrax-release data sets for each of the four spore dosages. The parameters were generated by averaging the probabilities obtained from files of a specific dosage in the training set. Once these probabilities specific to a dosage were obtained, the probabilities were averaged across the four different dosages because, currently, PANDA does not model the dosage.

The results of using the optimized person model on the data sets described in Section 4.2 are shown in Figure 18.7.

As expected, the optimized model significantly improves on the detection time of the original model. At zero false positives, the average detection time is approximately 127, 63, 44, and 38 hours for the corresponding simulated attack concentrations of 0.015625, 0.125, 0.5, and 1.0. The average improvement in detection time over the original model is 5, 21, 14, and 8 hours, respectively, for the four attack concentrations given above. The maximum widths of the 95% confidence intervals for the detection times at concentrations 0.015625, 0.125, 0.5, and 1.0 are ± 4.38,4.07, 2.15, and 1.62, respectively.

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