2017/02/25 by Rui Castro, Castro, Rui M., Ervin Tánczos +1
Computer Science · Decision Sciences · Economics, Econometrics and Finance · #Advanced Statistical Process Monitoring #Complex Systems and Time Series Analysis #Distributed Sensor Networks and Detection Algorithms #FOS: Mathematics #Statistics Theory (math.ST)
paper · pdf · doi:10.48550/arxiv.1702.07899
openalex publication_date 2017/02/25 · openalex created_date 2025/10/24 · openalex updated_date 2026/07/28
In this paper we investigate the problem of detecting dynamically evolving\nsignals. We model the signal as an n dimensional vector that is either zero\nor has s non-zero components. At each time step t\∈ \ℕ the\nnon-zero components change their location independently with probability p.\nThe statistical problem is to decide whether the signal is a zero vector or in\nfact it has non-zero components. This decision is based on m noisy\nobservations of individual signal components collected at times t=1,\…,m.\nWe consider two different sensing paradigms, namely adaptive and non-adaptive\nsensing. For non-adaptive sensing the choice of components to measure has to be\ndecided before the data collection process started, while for adaptive sensing\none can adjust the sensing process based on observations collected earlier. We\ncharacterize the difficulty of this detection problem in both sensing paradigms\nin terms of the aforementioned parameters, with special interest to the speed\nof change of the active components. In addition we provide an adaptive sensing\nalgorithm for this problem and contrast its performance to that of non-adaptive\ndetection algorithms.\n