Estimating significance in observations of variable and transient gamma-ray sources

The standard method for estimating the statistical significance of a gamma-ray source detection is that introduced by Li & Ma (1983), Eq. (17). In observing sources with time-dependent light curves, one can improve on this method by including approximate a priori knowledge of the source temporal behavior. A maximum-likelihood-based approach is suggested that provides an improvement in sensitivity with respect to the Li & Ma technique. The method is demonstrated by applying it to Monte Carlo simulations of gamma-ray burst observations with parameters chosen to reproduce the performance of current generation imaging air Cherenkov telescopes (IACTs). One particular example of a simulated burst observation near the current-generation IACT detection threshold results in a sensitivity improvement of approximately 25% . It is also shown that this method can work with highly variable light curves without much computational complexity, and that the sensitivity gain is robust against uncertainties in the a priori-defined light curve.