Distribution of the likelihood ratio in fermi gamma ray models
Degree GrantorUniversity of Canterbury
Degree NameMaster of Science
Gamma rays, the highest frequency component of the electromagnetic spectrum, are produced by the highest energy objects in the universe. The list of sources includes pulsars, active galactic nuclei, cosmic ray interactions, and as some have suggested dark matter. The Fermi Large Area Telescope was launched into orbit in 2008 to collect all-sky gamma ray data to investigate the mechanisms and sources that generate these particles.
Models are fit to the data through the use of the maximum likelihood method, in which a statistical algorithm finds the most likely model parameters that generated the data. When comparing two models to the same data, the likelihood ratio is developed that gives an indication as to how well the models explain the data.
In some problems, particularly in the detection of point sources against a background, it is of interest to compare the best fitting model to data with and without a point source present. In this case, the likelihood ratio that is used will determine whether there is a statistically significant source present.
This study will motivate the use of the test statistic and examine the asymptotic distribution of the statistic when comparing models. This will then be extended to consider a multiband analysis of data, and how the test statistic used is distributed in these cases. Using Monte Carlo techniques, the asymptotic distributions of the test statistic will be validated. This will be achieved within the FermiTools suite using the Fermi Science Support Center recommended procedures in fitting models to gamma ray data.