  Bayesian modeling techniques enable sensitivity analyses that incorporate
detailed expectations regarding future experiments. A model-based approach also
allows one to evaluate inferences and predicted outcomes, by calibrating (or
measuring) the consequences incurred when certain results are reported. We
present procedures for calibrating predictions of an experiment's sensitivity
to both continuous and discrete parameters. Using these procedures and a new
Bayesian model of the $\beta$-decay spectrum, we assess a high-precision
$\beta$-decay experiment's sensitivity to the neutrino mass scale and ordering,
for one assumed design scenario. We find that such an experiment could measure
the electron-weighted neutrino mass within $\sim40\,$meV after 1 year (90\%
credibility). Neutrino masses $>500\,$meV could be measured within
$\approx$5meV. Using only $\beta$-decay and external reactor neutrino data, we
find that next-generation $\beta$-decay experiments could potentially constrain
the mass ordering using a two-neutrino spectral model analysis. By calibrating
mass ordering results, we identify reporting criteria that can be tuned to
suppress false ordering claims. In some cases, a two-neutrino analysis can
reveal that the mass ordering is inverted, an unobtainable result for the
traditional one-neutrino analysis approach.
