Statistical analysis of detection of, and upper limits on, dark matter lines

Abstract

In this note we present calculations of coverage and power for three different methods which could be used to calculate upper limits and/or claim discovery in a GLAST‐LAT search for a dark matter line. The methods considered are Profile Likelihood, Bayesian factors and likelihood ratio confidence intervals and the calculations are done considering a simple benchmark model of two uncorrelated Poissonian measurements. Profile likelihood has the best coverage properties, the standard χ2 test the worst. For the power, the situation is vice‐versa. In choosing a method one has to consider the false detection rate (1 ‐ coverage) and counterweigh it to the possible achievable power.