  A full energy and flavor-dependent analysis of the three-year high-energy
IceCube neutrino events is presented. By means of multidimensional fits, we
derive the current preferred values of the high-energy neutrino flavor ratios,
the normalization and spectral index of the astrophysical fluxes, and the
expected atmospheric background events, including a prompt component. A crucial
assumption resides on the choice of the energy interval used for the analyses,
which significantly biases the results. When restricting ourselves to the ~30
TeV - 3 PeV energy range, which contains all the observed IceCube events, we
find that the inclusion of the spectral information improves the fit to the
canonical flavor composition at Earth, (1:1:1), with respect to a single-energy
bin analysis. Increasing both the minimum and the maximum deposited energies
has dramatic effects on the reconstructed flavor ratios as well as on the
spectral index. Imposing a higher threshold of 60 TeV yields a slightly harder
spectrum by allowing a larger muon neutrino component, since above this energy
most atmospheric tracklike events are effectively removed. Extending the
high-energy cutoff to fully cover the Glashow resonance region leads to a
softer spectrum and a preference for tau neutrino dominance, as none of the
expected electron antineutrino induced showers have been observed so far. The
lack of showers at energies above 2 PeV may point to a broken power-law
neutrino spectrum. Future data may confirm or falsify whether or not the
recently discovered high-energy neutrino fluxes and the long-standing detected
cosmic rays have a common origin.
