Self-calibrating the look-elsewhere effect: Fast evaluation of the statistical significance using peak heights
- Journal Article
In experiments where one searches a large parameter space for an anomaly, one often finds many spurious noise-induced peaks in the likelihood. This is known as the look-elsewhere effect, and must be corrected for when performing statistical analysis. This paper introduces a method to calibrate the false alarm probability (FAP), or p-value, for a given dataset by considering the heights of the highest peaks in the likelihood. Specifically, we derive an equation relating the global p-value to the rank and height of local maxima. In the simplest form of self-calibration, the look-elsewhere-corrected χ2 of a physical peak is approximated by the χ2 of the peak minus the χ2 of the highest noise-induced peak, with accuracy improved by considering lower peaks. In contrast to alternative methods, this approach has negligible computational cost as peaks in the likelihood are a byproduct of every peak-search analysis. We apply to examples from astronomy, including planet detection, periodograms, and cosmology. Show more
Journal / seriesMonthly Notices of the Royal Astronomical Society
Pages / Article No.
PublisherOxford University Press
SubjectAstroparticle physics; Methods: data analysis; Methods: statistical; Planets and satellites: detection; Planetary systems; Inflation
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