Theory and practice of nonparametric detection

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The scan statistic, or matched filter, has been extensively used for detection tasks. In many instances, a parametric model is assumed for simplicity and computational limitations. Also, various parametric settings for detection have been studied over the years. In particular, the investigator has done a study that establishes minimax rates for a large variety of problems and proves that the scan statistic achieves the optimal rate. However, most detection problems are nonparametric in nature, making it important to gain similar insight into nonparametric detection problems. By studying the problem of detection on graphs and drawing connections with Statistical Mechanics, the investigator brings a new understanding of such problems. The investigator also designs flexible graphical structures based on multiscale ideas to be the corner stone for developing new tools in various applied settings.The problem of detection arises in a wide variety of settings such as in analyzing galaxy catalogs; object tracking; road tracking; satellite imagery, which includes detecting man-made objects, detecting ships and fires; environment monitoring, which includes controlling pollution levels of water sources, detection of disease outbreaks and detection/localization of whales in the Ocean from acoustic data. The investigator studies the theoretical properties of the scan statistic in more complex (nonparametric) models for such detection tasks. Though the scan statistic has been extensively used in virtually all such problems, its behavior is mostly known under rather simplified (parametric) assumptions. Further, the investigator develops new tools for implementing the scan statistic in such complex detection settings. Such efficient tools are currently needed in many Scientific and Engineering fields, such as Astrophysics, in detecting galaxy clusters.