Neutrino statistics in a single pixel

The IceCube data at high energies is so sparse that we cannot afford to throw away information by reducing the data to averages. In our analysis, we therefore model not only the mean neutrino flux, but the entire probability distribution of this flux. We show that the expected neutrino event rates from rare sources are suppressed by the skewness of the flux distribution, weakening upper limits on their contributions to the observed flux by up to half an order of magnitude for our model of blazars. We also predict that the contribution from our model of star-forming galaxies appears completely diffuse and isotropic in IceCube, and forecast an inevitable null result for SFG γ/ν cross-correlation studies.