  Given the precision of current neutrino data, priors still impact noticeably
the constraints on neutrino masses and their hierarchy. To avoid our
understanding of neutrinos being driven by prior assumptions, we construct a
prior that is mathematically minimally informative. Using the constructed
uninformative prior, we find that the normal hierarchy is favoured but with
inconclusive posterior odds of 5.1:1. Better data is hence needed before the
neutrino masses and their hierarchy can be well constrained. We find that the
next decade of cosmological data should provide conclusive evidence if the
normal hierarchy with negligible minimum mass is correct, and if the
uncertainty in the sum of neutrino masses drops below 0.025 eV. On the other
hand, if neutrinos obey the inverted hierarchy, achieving strong evidence will
be difficult with the same uncertainties. Our uninformative prior was
constructed from principles of the Objective Bayesian approach. The prior is
called a reference prior and is minimally informative in the specific sense
that the information gain after collection of data is maximised. The prior is
computed for the combination of neutrino oscillation data and cosmological data
and still applies if the data improve.
