  The limits of the nuclear landscape are determined by nuclear binding
energies. Beyond the proton drip lines, where the separation energy becomes
negative, there is not enough binding energy to prevent protons from escaping
the nucleus. Predicting properties of unstable nuclear states in the vast
territory of proton emitters poses an appreciable challenge for nuclear theory
as it often involves far extrapolations. In addition, significant discrepancies
between nuclear models in the proton-rich territory call for quantified
predictions. With the help of Bayesian methodology, we mix a family of nuclear
mass models corrected with statistical emulators trained on the experimental
mass measurements, in the proton-rich region of the nuclear chart. Separation
energies were computed within nuclear density functional theory using several
Skyrme and Gogny energy density functionals. We also considered mass
predictions based on two models used in astrophysical studies. Quantified
predictions were obtained for each model using Bayesian Gaussian processes
trained on separation-energy residuals and combined via Bayesian model
averaging. We obtained a good agreement between averaged predictions of
statistically corrected models and experiment. In particular, we quantified
model results for one- and two-proton separation energies and derived
probabilities of proton emission. This information enabled us to produce a
quantified landscape of proton-rich nuclei. The most promising candidates for
two-proton decay studies have been identified. The methodology used in this
work has broad applications to model-based extrapolations of various nuclear
observables. It also provides a reliable uncertainty quantification of
theoretical predictions.
