Detection with scan statistics and average likelihood ratio: Methodology

该项目将研究和比较探测集群或“热点”的各种方法。它将建立关于平均似然比统计量的严格结果，最近在经验上声称该统计量优于扫描统计量。研究人员将得出指导方针，以决定什么时候其中一个比另一个更可取。该项目还将审查各种近似方案如何在能力和计算复杂性方面影响平均似然比统计的性能。近年来，由于生物监测、放射性材料检测或非法集装箱运输检测等各个领域出现的重要问题，空间集群或“热点”的检测问题受到了相当大的关注。最近的经验结果表明，通常用于这些目的的统计数据是次优的，可以通过不同的标准来改进。该项目将对这一经验发现进行严格的数学调查，并将得出指导方针，以决定在哪些情况下一种方法比另一种方法更可取。

The project will study and compare various methods to detect clusters or `hot spots'. It will establish rigorous results about the average likelihood ratio statistic, which has recently been claimed on empirical grounds to be superior to the scan statistic. The investigator will derive guidelines for deciding when one is preferable to the other. The project will also examine how various approximation schemes affect the performance of the average likelihood ratio statistic in terms of power and computational complexity.The problem of detecting spatial clusters or `hot spots' has received considerable attention in recent years, due to emerging important problems in various areas such as biosurveillance, the detection of radioactive materials, or the detection of illicit container shipments. Recent empirical findings suggest that the statistic that is commonly used for these purposes is suboptimal and can be improved upon by a different criterion. This project will perform a rigorous mathematical investigation of this empirical finding and will derive guidelines for deciding in which cases one methodology is preferrable to the other.