Comparison of Experimental Ultrahigh Energy Cosmic Ray Spectra using the Bayes Factor

Abstract:

A frequent problem in ultrahigh energy cosmic ray physics is the comparison of energy spectra. Given two or more measurements of the energy spectrum, the question is whether the spectra agree within their statistical and systematic uncertainties. We develop a method to directly compare two different energy spectra for ultrahigh enery cosmic rays that takes into account systematic errors and does not require the introduction of theoretical models for the shape of the energy spectrum. The consistency between the observations is expressed in terms of a Bayes Factor, a standard statistic defined as the ratio of a separate parent source hypothesis to a single parent source hypothesis. The method can be used to compare enery spectra measured by different experiments, or when comparing the energy spectra for different regions of the sky.

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