  It is possible that ultra-high energy cosmic rays (UHECRs) are generated by
active galactic nuclei (AGNs), but there is currently no conclusive evidence
for this hypothesis. Several reports of correlations between the arrival
directions of UHECRs and the positions of nearby AGNs have been made, the
strongest detection coming from a sample of 27 UHECRs detected by the Pierre
Auger Observatory (PAO). However, the PAO results were based on a statistical
methodology that not only ignored some relevant information (most obviously the
UHECR arrival energies but also some of the information in the arrival
directions) but also involved some problematic fine-tuning of the correlation
parameters. Here we present a fully Bayesian analysis of the PAO data
(collected before 2007 September), which makes use of more of the available
information, and find that a fraction F_AGN = 0.15^(+0.10)_(-0.07) of the
UHECRs originate from known AGNs in the Veron-Cetty & Veron (VCV) catalogue.
The hypothesis that all the UHECRs come from VCV AGNs is ruled out, although
there remains a small possibility that the PAO-AGN correlation is coincidental
(F_AGN = 0.15 is 200 times as probable as F_AGN = 0.00).
