  We perform a joint analysis of current data from cosmology and laboratory
experiments to constrain the neutrino mass parameters in the framework of
bayesian statistics, also accounting for uncertainties in nuclear modeling,
relevant for neutrinoless double $\beta$ decay ($0\nu2\beta$) searches. We find
that a combination of current oscillation, cosmological and $0\nu2\beta$ data
constrains $m_{\beta\beta}~<~0.045\,\mathrm{eV}$ ($0.014 \, \mathrm{eV} <
m_{\beta\beta} < 0.066 \,\mathrm{eV}$) at 95\% C.L. for normal (inverted)
hierarchy. This result is in practice dominated by the cosmological and
oscillation data, so it is not affected by uncertainties related to the
interpretation of $0\nu2\beta$ data, like nuclear modeling, or the exact
particle physics mechanism underlying the process. We then perform forecasts
for forthcoming and next-generation experiments, and find that in the case of
normal hierarchy, given a total mass of $0.1\,$ eV, and assuming a
factor-of-two uncertainty in the modeling of the relevant nuclear matrix
elements, it will be possible to measure the total mass itself, the effective
Majorana mass and the effective electron mass with an accuracy (at 95\% C.L.)
of $0.05$, $0.015$, $0.02\,\mathrm{eV}$ respectively, as well as to be
sensitive to one of the Majorana phases. This assumes that neutrinos are
Majorana particles and that the mass mechanism gives the dominant contribution
to $0\nu2\beta$ decay. We argue that more precise nuclear modeling will be
crucial to improve these sensitivities.
