Significance in gamma-ray astronomy - the Li & Ma problem in Bayesian statistics

The significance of having detected an astrophysical gamma ray source is usually calculated by means of a formula derived by Li & Ma in 1983. We solve the same problem in terms of Bayesian statistics, which provides a logically more satisfactory framework. We do not use any subjective elements in the present version of Bayesian statistics. We show that for large count numbers and a weak source the Li & Ma formula agrees with the Bayesian result. For other cases the two results differ, both due to the mathematically different treatment and the fact that only Bayesian inference can take into account prior knowldege.