The origins of ultra-high energy cosmic rays ( UHECRs ) remain an open question .
Several attempts have been made to cross-correlate the arrival directions of the UHECRs with catalogs of potential sources , but no definite conclusion has been reached .
We report a Bayesian analysis of the 69 events from the Pierre Auger Observatory ( PAO ) , that aims to determine the fraction of the UHECRs that originate from known AGNs in the Veron-Cety & Veron ( VCV ) catalog , as well as AGNs detected with the Swift Burst Alert Telescope ( Swift-BAT ) , galaxies from the 2MASS Redshift Survey ( 2MRS ) , and an additional volume-limited sample of 17 nearby AGNs .
The study makes use of a multi-level Bayesian model of UHECR injection , propagation and detection .
We find that for reasonable ranges of prior parameters , the Bayes factors disfavour a purely isotropic model .
For fiducial values of the model parameters , we report 68 % credible intervals for the fraction of source originating UHECRs of 0.09 ^ { +0.05 } _ { -0.04 } , 0.25 ^ { +0.09 } _ { -0.08 } , 0.24 ^ { +0.12 } _ { -0.10 } , and 0.08 ^ { +0.04 } _ { -0.03 } for the VCV , Swift-BAT and 2MRS catalogs , and the sample of 17 AGNs , respectively .