Observational information on high-energy astrophysical neutrinos is being continuously collected by the IceCube observatory. However, the sources of neutrinos are still unknown. In this study, we use radio very-long-baseline interferometry (VLBI) data for a complete VLBI-flux-density limited sample of active galactic nuclei (AGN). We address the problem of the origin of astrophysical neutrinos with energies above 200 TeV in a statistical manner. It is found that AGN positionally associated with IceCube events have typically stronger parsec-scale cores than the rest of the sample. The post-trial probability of a chance coincidence is 0.2%. We select the four strongest AGN as highly probable associations: 3C 279, NRAO 530, PKS 1741-038, and PKS 2145+067. Moreover, we find an increase of radio emission at frequencies above 10 GHz around neutrino arrival times for several other VLBI-selected AGN on the basis of RATAN-600 monitoring. The most pronounced example of such behavior is PKS 1502+106. We conclude that AGN with bright Doppler-boosted jets constitute an important population of neutrino sources. High-energy neutrinos are produced in their central parsec-scale regions, probably in proton-photon interactions at or around the accretion disk. Radio-bright AGN that are likely associated with neutrinos have very diverse gamma-ray properties suggesting that gamma-rays and neutrinos may be produced in different regions of AGN and not directly related. A small viewing angle of the jet-disk axis is, however, required to detect either of them.
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