Theory and practice of nonparametric detection

扫描统计量或匹配滤波器已广泛用于检测任务。在许多情况下，假设参数模型是为了简单和计算限制。此外，各种参数设置的检测已经研究了多年。特别是，研究者已经做了一项研究，为各种各样的问题建立了极大极小率，并证明了扫描统计量达到了最优率。然而，大多数检测问题本质上是非参数的，因此获得对非参数检测问题的类似见解非常重要。通过对图形检测问题的研究，以及与统计力学的联系，研究者对这类问题有了新的认识。研究者还设计了基于多尺度思想的灵活图形结构，作为在各种应用环境中开发新工具的基石。探测问题出现在各种各样的环境中，比如分析星系目录；对象跟踪;道路跟踪;卫星图像，包括探测人造物体，探测船只和火灾；环境监测，其中包括控制水源的污染程度、检测疾病爆发和根据声学数据检测/定位海洋中的鲸鱼。研究者研究了扫描统计量在更复杂（非参数）模型中用于此类检测任务的理论性质。尽管扫描统计量已广泛用于几乎所有此类问题，但其行为大多是在相当简化的（参数）假设下已知的。此外，研究者开发了在这种复杂的检测设置中实现扫描统计的新工具。目前许多科学和工程领域，如天体物理学，都需要这种有效的工具来探测星系团。

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.