Comparing Cosmic Ray Energy Spectra Using a Bayes Factor

Abstract:

We develop a statistical method to compare energy spectra for ultra-high energy cosmic rays from different regions of the sky in the same experiment without reliance on agreement with a theoretical model of the energy spectra. The consistency between the two spectra is expressed in terms of a Bayes factor, defined here as the ratio of the likelihood of the two-parent source hypothesis to the likelihood of the one-parent source hypothesis. The Bayes factor allows for the calculation of the posterior odds ratio and correctly accounts for non-Gaussian uncertainties. An important application is the study of the energy spectrum in a region of the sky that contains one or more strong cosmic ray accelerators. If the sources are nearby and the flux is not subject to GZK suppression, the spectrum can potentially deviate significantly from the all-sky spectrum.

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