Is the bump significant? An axion-search example

Understand

Many experiments in physics involve searching for a localized excess over background expectations in an observed spectrum.

• If the background is known and there is Gaussian noise, the amount of excess of successive observations can be quantified by the runs statistic taking care of the look-elsewhere effect.
• The distribution of the runs statistic under the background model is known analytically but the computation becomes too expensive for more than about a hundred observations.
• This work demonstrates a principled high-precision extrapolation from a few dozen up to millions of data points.