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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.