It is known that the scan statistic with variable window size favors the detection of signals with small spatial extent and there is a corresponding loss of power for signals with large spatial extent. Recent results have shown that this loss is not inevitable: Using critical values that depend on the size of the window allows optimal detection for all signal sizes simultaneously, so there is no substantial price to pay for not knowing the correct window size and for scanning with a variable window size. This paper gives a review of the heuristics and methodology for such size-dependent critical values, their applications to various settings including the multivariate case, and recent results about fast algorithms for computing scan statistics.
翻译:众所周知,有可变窗口大小的扫描统计有利于在空间范围小的情况下探测信号,而且对空间范围大的信号也相应丧失了相应的功率。最近的结果显示,这一损失并非不可避免:使用视窗口大小而定的关键值,可以同时对所有信号大小进行最佳检测,因此,不知道正确的窗口大小和用可变窗口大小进行扫描没有重大代价。本文回顾了这种大小依赖的关键值的超自然学和方法,这些关键值在各种设置中的应用情况,包括多变量案例,以及计算扫描统计数据的快速算法的最新结果。