Spatial Inference in Large-Scale Sensor Networks via Multiple Hypothesis Testing

The identification of spatial regions exhibiting interesting, anomalous, or unexpected signal behavior is a fundamental task in many practical applications in signal processing and beyond. This thesis develops novel methodologies to solve this spatial inference problem based on multiple hypothesis testing, using data recorded by large-scale wireless sensor networks. The proposed methods identify these regions while rigorously controlling false positives through statistical guarantees in terms of the false discovery rate. The measurements are pre-processed locally at the nodes. Only local summary statistics are transmitted to a fusion center or cloud. This ensures that the valuable communication resources and node battery power are used efficiently. A flexible data-driven empirical Bayes framework is introduced to infer spatial signal behavior across a discrete spatial grid, enabling decision-making about the local state of the observed phenomenon for each grid point. The methods are agnostic to specific signal propagation models, and instead rely on broadly applicable statistical probability models. Novel techniques to estimate local false discovery rates based on the spectral method of moments and expectation-maximization are developed, which yield accurate inference results. These methods are computationally lightweight, handle quantized local statistics effectively, and achieve higher precision than existing approaches. The proposed framework is extended to include spatial priors, which further improves the detection power by exploiting the smoothness of spatial signals. Additionally, censoring is introduced to prevent uninformative sensor nodes from communicating. This reduces the number of transmissions significantly, thereby conserving energy and communication bandwidth, while maintaining inference result accuracy. A real-world implementation of a large-scale wireless sensor network for indoor people detection using relative humidity measurements is developed. This demonstrates the practical applicability of the methods proposed in this thesis. Finally, sequential spatial inference is proposed, enabling the iterative refinement of inference results over time. Nodes are selectively allowed to transmit additional data, which significantly improves the detection power with limited additional transmissions. Multiple algorithms for sequential transmission selection are proposed, including one that maximizes the expected immediate detection power. The contributions of this thesis provide a novel methodology for spatial inference in resource-constrained wireless sensor networks. Strict false discovery rate control ensures the reliability and objectivity of the results. These methods enable precise identification of spatially anomalous signal behavior and are directly applicable in a wide range of practical domains such as electromagnetic spectrum awareness, environmental monitoring, smart buildings, or radar-based target detection.