  We present a showcase for deriving bounds on the neutrino masses from
laboratory experiments and cosmological observations. We compare the
frequentist and Bayesian bounds on the effective electron neutrino mass m_beta
which the KATRIN neutrino mass experiment is expected to obtain, using both an
analytical likelihood function and Monte Carlo simulations of KATRIN. Assuming
a uniform prior in m_beta, we find that a null result yields an upper bound of
about 0.17 eV at 90% confidence in the Bayesian analysis, to be compared with
the frequentist KATRIN reference value of 0.20 eV. This is a significant
difference when judged relative to the systematic and statistical uncertainties
of the experiment. On the other hand, an input m_beta=0.35 eV, which is the
KATRIN 5sigma detection threshold, would be detected at virtually the same
level. Finally, we combine the simulated KATRIN results with cosmological data
in the form of present (post-WMAP) and future (simulated Planck) observations.
If an input of m_beta=0.2 eV is assumed in our simulations, KATRIN alone
excludes a zero neutrino mass at 2.2sigma. Adding Planck data increases the
probability of detection to a median 2.7sigma. The analysis highlights the
importance of combining cosmological and laboratory data on an equal footing.
