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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. In the simplest form of self-calibration, the look-elsewhere-corrected $chi^2$ of a physical peak is approximated by the $chi^2$ of the peak minus the $chi^2$ of the highest noise-induced peak. Generalizing this concept to consider lower peaks provides a fast method to quantify the statistical significance with improved accuracy. 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.
The cosmic optical background is an important observable that constrains energy production in stars and more exotic physical processes in the universe, and provides a crucial cosmological benchmark against which to judge theories of structure formati
Voronoi grids have been successfully used to represent density structures of gas in astronomical hydrodynamics simulations. While some codes are explicitly built around using a Voronoi grid, others, such as Smoothed Particle Hydrodynamics (SPH), use
This white paper describes the science case for Very Long Baseline Interferometry (VLBI) and provides suggestions towards upgrade paths for the European VLBI Network (EVN). The EVN is a distributed long-baseline radio interferometric array, that oper
The Large Synoptic Survey Telescope is designed to provide an unprecedented optical imaging dataset that will support investigations of our Solar System, Galaxy and Universe, across half the sky and over ten years of repeated observation. However, ex
Laboratory astrophysics and complementary theoretical calculations are the foundations of astronomy and astrophysics and will remain so into the foreseeable future. The impact of laboratory astrophysics ranges from the scientific conception stage for