On methods for correcting for the look-elsewhere effect in searches for new physics

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Title: On methods for correcting for the look-elsewhere effect in searches for new physics
Authors: Algeri, S
Van Dyk, DA
Conrad, J
Anderson, B
Item Type: Journal Article
Abstract: The search for new significant peaks over a energy spectrum often involves a statistical multiple hypothesis testing problem. Separate tests of hypothesis are conducted at different locations over a fine grid producing an ensemble of local p-values, the smallest of which is reported as evidence for the new resonance. Unfortunately, controlling the false detection rate (type I error rate) of such procedures may lead to excessively stringent acceptance criteria. In the recent physics literature, two promising statistical tools have been proposed to overcome these limitations. In 2005, a method to ``find needles in haystacks'' was introduced by Pilla et al. [1], and a second method was later proposed by Gross and Vitells [2] in the context of the ``look-elsewhere effect'' and trial factors. We show that, although the two methods exhibit similar performance for large sample sizes, for relatively small sample sizes, the method of Pilla et al. leads to an artificial inflation of statistical power that stems from an increase in the false detection rate. This method, on the other hand, becomes particularly useful in multidimensional searches, where the Monte Carlo simulations required by Gross and Vitells are often unfeasible. We apply the methods to realistic simulations of the Fermi Large Area Telescope data, in particular the search for dark matter annihilation lines. Further, we discuss the counter-intuitive scenario where the look-elsewhere corrections are more conservative than much more computationally efficient corrections for multiple hypothesis testing. Finally, we provide general guidelines for navigating the tradeoffs between statistical and computational efficiency when selecting a statistical procedure for signal detection.
Issue Date: 14-Dec-2016
Date of Acceptance: 23-Nov-2016
ISSN: 1748-0221
Publisher: IOP Publishing
Start Page: P12010
End Page: P12010
Journal / Book Title: Journal of Instrumentation
Volume: 11
Issue: 12
Copyright Statement: © 2016 IOP Publishing Ltd and Sissa Medialab srl
Sponsor/Funder: The Royal Society
Stockholm University
Commission of the European Communities
European Commission
Funder's Grant Number: WM110023
Keywords: Nuclear & Particles Physics
Publication Status: Published
Appears in Collections:Mathematics
Faculty of Natural Sciences

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