Because of the low photon detection rate and the extent of the PSF, statistical techniques are required to analyze EGRET data. Maximum likelihood (Mattox et al. 1995a) is used to estimate point source flux densities, source locations, and background model parameters. The likelihood of binned EGRET data is the product of the probability for each pixel
where
is the Poisson probability of observing counts in pixel ij when the number of counts predicted by the model is . The likelihood ratio test is used to determine the significance of point sources. The likelihood ratio test statistic is , where is the log of the likelihood of the data if a point source is included in the model, and is the log of the likelihood of the data without a point source. In the null hypothesis, TS is asymptotically distributed as for a source at a specific position. Mattox et al. (1995a) show that the corresponding significance is . Monte Carlo simulation and experience with flight data indicate that these techniques provide reliable results.