  The goal of this paper is to introduce a novel likelihood-based inferential
framework for axion haloscopes which is valid under the commonly applied
"rescanning" protocol. The proposed method enjoys short data acquisition times
and a simple tuning of the detector configuration. Local statistical
significance and power are computed analytically, avoiding the need of
burdensome simulations. Adequate corrections for the look-elsewhere effect are
also discussed. The performance of our inferential strategy is compared with
that of a simple method which exploits the geometric probability of rescan.
Finally, we exemplify the method with an application to a HAYSTAC type axion
haloscope.
