Value of information for spatially distributed systems: Application to sensor placement

This paper investigates how the value of information (VoI) metric can guide information collection and optimal sensor placement in spatially distributed systems. VoI incorporates relevant features to decision-making, such as uncertainty about the state of the system, precision of measurements, the availability of intervention actions, and the overall cost of managing the system. Spatially distributed systems also allow for information propagation, i.e. measurements collected at one location can be used to update knowledge at other related locations. In this paper, while restricting our attention to Gaussian random field and binary state models, we illustrate first how sensor placements depend on the decision-making problem to be addressed, as encoded in a problem-specific loss function, and second how the complexity of VoI computations is impacted by this loss function's characteristics. In doing so, we consider several loss functions and present computational techniques for evaluating VoI under them. Finally, we apply these techniques to efficiently optimize sensor placements by the VoI metric in two example applications.