Integrating Location Models with Bayesian Analysis to Inform Decision Making

In the present work, we locate sensors in water distribution networks and make inferences on the presence of contamination events based on sensor signals. We fully consider the imperfection of sensors, which means that sensors do provide false positive and false negative signals, and we propose a two-stage model by combining a facility location model with Bayesian networks to (1) identify optimal sensors locations and (2) infer the probability of the occurrence of a contamination event and the possible contamination source based on sensor signals, the probability of a contamination event being detected by the sensors given that there is a contamination event, and the probability of detecting a contamination event given that there is actually no such event (overall false positive rate). This two-stage model can also be used to construct the trade-offs between the number of sensors and the power (the false negative and false positive rates) of individual sensors while guaranteeing the performance (the probability of detecting random contamination events) of the sensor network system (all the sensors). The method can be generalized to address similar problems in deploying sensors in harsh environments.