Analyzing the Performance of Bayesian Aggregation Under Erroneous Environmental Beliefs

In gamma-ray source detection, Bayesian aggregation (BA) is a state-of-the-art framework for combining evidence from multiple sensor measurements to detect weak sources of gamma-ray radiation in complex environments. To accomplish this, BA relies on an estimate of a sensor’s response in both the source-absent and source-present scenarios. Due to the abundance of noisy environmental factors, a perfect estimate of the sensor’s response is difficult to obtain. In this article, we develop a novel theoretical analysis of BA that allows one to characterize detection performance (in terms of missed detections and false alarms) as a function of the believed and true sensor response models. This theoretical framework is a powerful tool for quickly evaluating the effect of erroneous beliefs without the need to perform time-consuming simulations. The latter part of this work presents a case study that showcases an application of this theoretical framework. With a simplified source injection model wherein only the true background radiation is unknown, we use the framework to analyze detection performance loss as a function of the bias in the total background rate estimation. Guided by these theoretical insights, we develop a novel extension to BA that decreases this bias by adaptively modeling the local background. Finally, using two real-world datasets of mobile gamma-ray sensors in an urban environment, we show increased detection performance when compared to non-adaptive BA.