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SUMMARY:Distribution-Free Detection of Structured Anomalies: Permutation a
 nd Rank-Based Scans - Rui Castro (Eindhoven)
DTSTART:20160212T160000Z
DTEND:20160212T170000Z
UID:TALK63643@talks.cam.ac.uk
CONTACT:Quentin Berthet
DESCRIPTION:The scan statistic is by far the most popular method for anoma
 ly detection\, being popular in syndromic surveillance\, signal and image 
 processing and target detection based on sensor networks\, among other app
 lications.  The use of scan statistics in such settings yields an hypothes
 is testing procedure\, where the null hypothesis corresponds to the absenc
 e of anomalous behavior.  If the null distribution is known calibration of
  such tests is relatively easy\, as it can be done by Monte-Carlo simulati
 on.  However\, when the null distribution is unknown the story is less str
 aightforward.  We investigate two procedures: (i) calibration by permutati
 on and (ii) a rank-based scan test\, which is distribution-free and less s
 ensitive to outliers.  A further advantage of the rank-scan test is that i
 t requires only a one-time calibration for a given data size making it com
 putationally much more appealing than the permutation-based test.  In both
  cases\, we quantify the performance loss with respect to an oracle scan t
 est that knows the null distribution.  We  show that using one of these ca
 libration procedures results in only a very small loss of power in the con
 text of a natural exponential family.  This includes for instance the clas
 sical normal location model\, popular in signal processing\, and the Poiss
 on model\, popular in syndromic surveillance. Numerical experiments furthe
 r support our theory and results (joint work with Ery Arias-Castro\, Meng 
 Wang (UCSD) and Ervin Tánczos (TU/e)).
LOCATION:MR12\, Centre for Mathematical Sciences\, Wilberforce Road\, Camb
 ridge.
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