Detecting the neutrino mass and mass hierarchy from global data
  In this paper, we have constrained the neutrino mass and mass hierarchy in
the $\Lambda$CDM cosmology with the neutrino mass hierarchy parameter $\Delta$,
which represents different mass orderings, by using the {\it Planck} 2015 + BAO
+ SN + $H_{0}$ data set, together with the neutrino oscillation and
neutrinoless double beta decay data. We find that the mass of the lightest
neutrinos and the total neutrino mass are no more than $0.035$eV and $0.133$ eV
at $95\%$ confidence level, respectively. Comparing the result of our joint
analysis with that obtained using cosmological data alone, we find that, by
adding the neutrino oscillation and neutrinoless double beta decay data, the
tendency for normal hierarchy has increased a lot. By means of importance
sampling, three other priors are taken into account, i.e., the flat logarithmic
prior on the absolute value of the neutrino hierarchy parameter $\Delta$, the
flat linear prior on the total neutrino mass $\Sigma m_{\nu}$, and the flat
logarithmic prior on $\Sigma m_{\nu}$. We find that the preference for the
normal hierarchy is in agreement whatever what kinds of priors we choose.
Finally, we make a Bayesian model analysis about four priors and we find that
flat-linear and the flat logarithmic priors on $\Sigma m_{\nu}$ are the most
favored priors.
