  We perform a global fit of the most relevant neutrinoless double beta decay
experiments within the standard model with massive Majorana neutrinos. Using
Bayesian inference makes it possible to take into account the theoretical
uncertainties on the nuclear matrix elements in a fully consistent way. First,
we analyze the data used to claim the observation of neutrinoless double beta
decay in Ge-76, and find strong evidence (according to Jeffrey's scale) for a
peak in the spectrum and moderate evidence for that the peak is actually close
to the energy expected for the neutrinoless decay. We also find a significantly
larger statistical error than the original analysis, which we include in the
comparison with other data. Then, we statistically test the consistency between
this claim with that of recent measurements using Xe-136. We find that the two
data sets are about 40 to 80 times more probable under the assumption that they
are inconsistent, depending on the nuclear matrix element uncertainties and the
prior on the smallest neutrino mass. Hence, there is moderate to strong
evidence of incompatibility, and for equal prior probabilities the posterior
probability of compatibility is between 1.3% and 2.5%. If one, despite such
evidence for incompatibility, combines the two data sets, we find that the
total evidence of neutrinoless double beta decay is negligible. If one ignores
the claim, there is weak evidence against the existence of the decay. We also
perform approximate frequentist tests of compatibility for fixed ratios of the
nuclear matrix elements, as well as of the no signal hypothesis. Generalization
to other sets of experiments as well as other mechanisms mediating the decay is
possible.
