Detection with scan statistics and average likelihood ratio: Methodology

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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.