Bayesian naturalness, simplicity, and testability applied to the $B-L$ MSSM GUT

Recent years have seen increased use of Bayesian model comparison to quantify notions such as naturalness, simplicity, and testability, especially in the area of supersymmetric model building. After demonstrating that Bayesian model comparison can resolve a paradox that has been raised in the literature concerning the naturalness of the proton mass, we apply Bayesian model comparison to GUTs, an area to which it has not been applied before. We find that the GUTs are substantially favored over the non-unifying puzzle model. Of the GUTs we consider, the $B-L$ MSSM GUT is the most favored, but the MSSM GUT is almost equally favored.