  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. 
Combining and comparing neutrinoless double beta decay experiments using   different nuclei