  A flux of extra-terrestrial neutrinos at energies $\gg10^{15}$ eV has the
potential to serve as a cosmological probe of the high-energy universe as well
as tests of fundamental particle interactions. Cosmogenic neutrinos, produced
from the interactions of ultra-high energy cosmic rays (UHECRs) with cosmic
photon backgrounds, have been regarded as a guaranteed flux. However, the
expected neutrino flux depends on the composition of UHECRs at the highest
energies; heavier nuclei result in lower neutrino fluxes compared to lighter
nuclei and protons. The objective of this study is to estimate the range of
cosmogenic neutrino spectra consistent with recent cosmic-ray spectral and
compositional data using a fully inferential Bayesian approach. The study
assumes a range of source distributions consistent with astrophysical sources,
the flux and composition of cosmic rays, and detector systematic uncertainties.
The technique applied to this study is the use of an affine-invariant Markov
Chain Monte Carlo, which is an effective Bayesian inference tool for
characterizing multi-dimensional parameter spaces and their correlations.
