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P. L. Nolan (Stanford University)
Although GLAST will detect many more photons than EGRET, most analyses will be carried out with a small number of photons. Thus approximate statistical methods, such as chi-squared tests, will not be applicable. It will be necessary to use the full Poisson likelihood.
Two factors will make the GLAST analysis more complex than EGRET's. First, the field of view is very large. The width of the point spread function varies greatly from the center to the edge. This is in addition to the well-known energy dependence. Second, GLAST will operate in a scanning mode, so that each point source will sweep across the field of view for 20-40 minutes of each 90-minute orbit. EGRET would stare at small portions of the sky for 1-3 weeks at a time, and data from an entire exposure could be added together. Each GLAST photon will have its own point spread function, so each will need to be analyzed separately.
Common analyses, such as finding point sources, determining the brightness of known sources, or spectrum fitting, will all require calculating likelihood functions. Each calculation will be a multidimensional integral. These integrals are displayed in all their glory. For some common calculations there are techniques which can be used to simplify the process.
This work was supported by NASA contract NAS5-00147.
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