Information and Inference for Point Processes

This book develops principled methods for sensor management when an uncertain scene is represented by a point process. This book shows how information theory, estimation bounds, population error measures, and decision theory can be used to compare and select sensing actions. It develops entropy and mutual information for point-process states, information contraction under observation and compression, Fisher information and Cramér-Rao and Van Trees bounds, dependence-aware precision, quadratic and Mahalanobis population errors, Bayes risk, and closed-loop and distributed sensing. The book includes information measures uncertainty reduction; estimation bounds assess attainable precision; population errors assess estimated configurations; and decision risk measures task consequences. The book explains when these criteria agree, when they differ, and how they guide multi-target surveillance, sensor scheduling, waveform and aperture selection, distributed fusion, point-source sensing, and communication-constrained networks. It is intended for researchers and doctoral readers in statistical signal processing, communications, tracking, sensor fusion, and adaptive sensing.