Self-calibrating the look-elsewhere effect: fast evaluation of the statistical significance using peak heights

In experiments where one searches a large parameter space for an anomaly, often finds many spurious noise-induced peaks in the likelihood. This is known as look-elsewhere effect, and must be corrected when performing statistical analysis. paper introduces method to calibrate false alarm probability (FAP), or $p$-value, given dataset by considering heights of highest simplest form self-calibration, look-elsewhere-corrected $\chi^2$ physical peak approximated minus peak. Generalizing this concept consider lower provides fast quantify significance with improved accuracy. contrast alternative methods, approach has negligible computational cost likelihood are byproduct every peak-search We apply examples from astronomy, including planet detection, periodograms, cosmology.