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The scan statistic is by far the most popular method for anomaly detection,being popular in syndromic surveillance, signal and image processing, andtarget detection based on sensor networks, among other applications. The use ofthe scan statistics in such settings yields a hypothesis testing procedure,where the null hypothesis corresponds to the absence of anomalous behavior. Ifthe null distribution is known, then calibration of a scan-based test isrelatively easy, as it can be done by Monte Carlo simulation. When the nulldistribution is unknown, it is less straightforward. We investigate twoprocedures. The first one is a calibration by permutation and the other is arank-based scan test, which is distribution-free and less sensitive tooutliers. Furthermore, the rank scan test requires only a one-time calibrationfor a given data size making it computationally much more appealing. In bothcases, we quantify the performance loss with respect to an oracle scan testthat knows the null distribution. We show that using one of these calibrationprocedures results in only a very small loss of power in the context of anatural exponential family. This includes the classical normal location model,popular in signal processing, and the Poisson model, popular in syndromicsurveillance. We perform numerical experiments on simulated data furthersupporting our theory and also on a real dataset from genomics.

Distribution-Free Detection of Structured Anomalies: Permutation and Rank-Based Scans