In gamma-ray astronomy, the ability to combine data from multiple observatories that sample different regions of the gamma-ray spectrum is crucial to understanding processes–such as particle acceleration and diffusion–that take place in and around astrophysical phenomena. Ground-based gamma-ray observatories therefore provide an important complement to NASA’s Fermi Gamma-Ray Space Telescope (FGST).

In particle astrophysics, extended maximum likelihood methods, which can be used to derive the fractional contributions as well as spatial and spectral parameters of multiple data components with different astrophysical origins, also provide a natural framework for combining data from multiple observatories. Such techniques are already the standard approach for analyzing data from the FGST. Our research seeks to address the problems that arise when applying the technique of binned extended maximum likelihoods to data procured for ground-based gamma-ray astronomy. These problems stem from the fact that gamma-ray astronomy data spaces are largely dominated not by gamma-rays, but by cosmic rays. The large uncertainties associated with Monte Carlo models of cosmic ray background in conjunction with the low uncertainties of gamma-ray models result in a data space comprising regions of high uncertainty and other regions of low uncertainty. A data space of this form introduces serious mathematical issues for present maximum likelihood methods. Our objective is to run a series of tests that emulate this problematic scenario in order to better understand the statistical considerations that must be made for maximum likelihood analysis of gamma-ray data.