Statistical data analysis for gamma-ray astronomy

Abstract

Significance testing, parameter estimation and sensitivity calculations for γ-ray telescopes are discussed for single ‘on-off” astronomical observations. Four widely used significance test methods are examined by Monte-Carlo simulations. The Maximum Likelihood Ratio Method is found to consistently over-estimate the significance of an observation by a few percents whereas the Fisher's Exact Test is shown to be slightly conservative and always under-estimates the significance by about the same amount when the reported significance is about 3σ and therefore it is preferred for γ-ray astronomy applications. Two methods for constructing a confidence interval and an upper limit for γ-ray source counts are discussed. It is found that the method based on the Smooth Transformation provides slightly better estimations. A new formula for the calculation of the sensitivity of a γ-ray telescope is presented, in contrast to the widely accepted one, and their statistical meanings are explained in detail.